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Asked about the state of the relationship between the UK and US, the prime minister said he believes it is “as strong as it’s ever been”.

Burnham has travelled to New York with his wife, Marie-France Van Heel, for a day of diplomacy and a speech to the UN General Assembly, which is expected to focus on the opportunities and dangers associated with artificial intelligence (AI).

He said: “I will be making the case for closer international co-operation on AI, a just and lasting peace in Ukraine, and renewed efforts to bring an end to the conflict in the Middle East because what happens abroad impacts each and every one of us at home.”

The prime minister will also announce the start of work on a new AI and Autonomy partnership between the UK and the US, focused on protecting critical national infrastructure using AI tech.

Lib Dem leader Sir Ed Davey is expected to criticise this plan at the final day of his party’s conference, saying it “doesn’t come close to meeting the scale of the threat” and “only risks making us more dependent on a Trump administration in the pocket of the tech bros”.

He will also call for a global pause on superintelligent AI and propose a new International AI Safety Agency.

His criticisms come after a series of stark warnings from the AI industry about the technology’s possible dangers.

For a new British prime minister, the first meeting with a US president has always been a pivotal encounter, but officials are well aware of the added jeopardy of a public appearance alongside the most unpredictable president in American history.

In advance of the meeting, the UK revealed that the UK and the US have, for the first time, fired an American torpedo from a British undersea drone in a military exercise.

The torpedo, described as “heavyweight” by UK officials, is “designed to sink ships and deep diving submarines”, Downing Street said.

It was launched in UK waters last week from a 12-metre long undersea drone called Excalibur, made in Plymouth.

It is the first time either the UK or the US have launched a torpedo from an uncrewed underwater vessel, rather than a crewed submarine, and is seen as a breakthrough in attempts to protect vital infrastructure such as deep sea data cables.

“Our work together already shows what can be achieved when our two countries combine our expertise and innovation,” the prime minister said.

Burnham was also asked by reporters about the UK government seeking to hand over the Chagos Islands to Mauritius and pay to lease back the joint US-UK military base on Diego Garcia.

It was confirmed in April that the deal had been paused indefinitely because of Trump pulling his support.

Burnham spoke to the Mauritian prime minister, Navin Ramgoolam, on Monday.

He was asked by reporters to outline what he had told Ramgoolam, whether he supported the deal and if he had a plan to convince Trump to back it.

Burnham replied: “I said that we remain determined to secure the long-term operation of the base, which is crucial to our security and that of our allies.

“The assurance I gave was I will work towards a resolution, at the moment we don’t have that, but I gave an assurance that I would commit to working towards one.”

NHS GP Dr Amir Khan says a common method for dealing with nosebleeds is not correct

Dr Amir Khan has offered guidance on how to properly treat a nosebleed, revealing that many people have been receiving incorrect advice. The well-known TV doctor and NHS GP, recognised for his regular slots on ITV’s This Morning and Lorraine, discussed the matter with his followers on the latest instalment of his podcast, No Appointment Necessary.

His explanation may come as a surprise to some who have been instructed to do something entirely different when dealing with a nosebleed. Co-host Cherry Healey appeared to be among them, as she questioned him about the advice people have given her for managing a nosebleed.

She said: “You know when someone gets a nosebleed, they always get told to put their head back. It’s so awful when you get a nosebleed and someone tells you that because it’s what you don’t want to do. Is that true?”

The doctor responded: “No. It used to be that, but it’s not head back. It’s head forward. Yeah, because if you go back, you could swallow the blood and then cause all sorts of issues.”

He then outlined what you should do instead, saying: “First of all, you want to pinch the soft bit of your nose just underneath the bone. I’m talking like this now because I’m doing it. So pinch that bit as tight, as tight as you can and then lean forward.

“So head between your knees or lean as far forward as you can for, you’ve guessed it, 15 minutes. 15 to 20 minutes is when anything is bleeding.

“That’s how long you need to put pressure on it.” Cherry then replied: “Because that’s how long it takes to clot.”

His advice is important because many people have been given incorrect advice. McGill University in Canada says the tilt-the-head-back method is a ‘common misconception’.

Its website states: “First aid standards have changed throughout the years, making it difficult to keep up with the right practice. Tilting your head backwards is common misconception. Currently, Red Cross standards and most clinicians inform us to sit neutral, tilt head slightly forward, pinch the bridge of the nose, and wait for 10-15 minutes.”

NHS advice on what to do if you have a nosebleed

The NHS website advises that if you experience a nosebleed, you should sit down and lean forward, with your head tilted forward and your mouth open; pinch your nose just above your nostrils for 10 to 15 minutes; and breathe through your mouth. It adds: “Holding an icepack (or a bag of frozen peas wrapped in a tea towel) on the top of the nose may help reduce the blood flow. But the evidence to show it works is not very strong.”

It also provides guidance on what to do for the 24 hours following a nosebleed. To reduce the likelihood of another nosebleed, for 24 hours afterwards, it recommends you should try not to pick your nose, blow it, or pick any scabs.

It also suggests avoiding lying down flat, doing any heavy lifting or strenuous exercise, or consuming hot drinks or alcohol.

Dr Amir Khan tells patients what not to say in his practice

The doctor’s guidance comes a day after he shared with Instagram followers a list of things he does not want to hear from his patients. The reassuring post, which we reported about on Friday, stated people should not apologise for their weight, their toenails, or their hairy legs.

He said: “Please, you’re having a medical examination, I am not bothered about anything else. “He also said people should not apologise if they feel the need to cry, or if they cannot remember the name of their tablets. And he said: “Please don’t say things like I’m sorry to waste your time.

“If something is worrying you enough that you’ve come to make an appointment to come and see me, that’s what I’m here for.” He concluded by noting: “The only thing that I care about is that you feel able to tell me what’s really going on.

“Because the thing you might be embarrassed about might actually be really important, and I can’t help something you feel ashamed to tell me. So, come as you are, cry if you need to, don’t shave anything on my account, and please stop apologising for just being a patient. You’re not an inconvenience, you’re literally the reason why I’m here.”

Find episodes of the podcast on YouTube, Apple or other platforms.

The EU’s Entry/Exit System (EES) is now in place and, while most travellers are familiar with the biometric checks, a travel expert warns it’s the lesser-known rules that are catching people out

Lots of tourists may be feeling nervous about travel delays this year after reports emerged airports could face a new wave of chaos. Some of this worry has stemmed from the fact that EES, which stands for Entry/Exit System, has come into place this year – this is an automated digital IT system developed by the European Union to register non-EU nationals each time they cross the external borders of participating European nations.

However, if you’re due to travel and want to know what to expect, there’s some expert advice you may want to take on board. A few simple travel tips can make all the difference to helping the start of your holiday go more smoothly.

It’s not the first time the subject has been highlighted to travellers either. Previously, it was reported how UK travellers were preparing for border delays due to the system.

What’s it all about?

This year marked the first summer that the EU’s new Entry/Exit System (EES) has been in operation and, while you’ve likely seen reports about lengthier queues at certain airports, for most holidaymakers, it’s simply another aspect of travelling that requires a bit of adjustment. If you’re bound for countries such as Spain, France, Italy, Portugal or Greece, here’s what you need to be aware of before you fly.

Travel expert Ricky Durrance, of package holiday specialists Teletext Holidays, says that, while everyone’s heard about the biometric checks, it’s the minor regulations that are tripping people up. He issued some guidance to help travellers.

Don’t get caught out

One of the least well-known aspects of EES is that your registration is tied to your passport, not to you personally. So, if you’ve renewed your passport since you last visited an EU country, you’ll be treated as a first-time traveller, even if you’ve previously completed biometric registration.

That means providing fingerprints and a facial scan once again at the border. So, you’ll need to allow extra time.

“Many travellers would assume once they’re already in the system that’s job done,” said Ricky. “But EES is tied to the passport, not the person, so don’t be caught out by unexpected enrolment.”

Can things be sped up?

Depending on where you’re departing from, you may even be able to complete part of the process before you set off. The EU’s free Travel to Europe app allows travellers using participating border crossings to upload passport details and a facial image up to 72 hours before departure, helping make the process even smoother.

It’s worth checking whether your airport supports it before you travel. If you’ve booked a package holiday, border delays can have a knock-on effect on transfers, so check with your travel agent whether your departure airport supports early enrolment and allow extra time on arrival.

What about kids?

Families should also bear in mind that every traveller has their own EES record, children included. Each child will require their own passport and facial image check, although under-12s are exempt from providing fingerprints, which helps to speed things up slightly.

It doesn’t apply in every country

The good news is that EES isn’t applicable across the board. Popular holiday hotspots including Turkey, Egypt, Morocco and Tunisia fall outside the Schengen Area, meaning British tourists heading there won’t need to complete EES checks.

For anyone weighing up destinations, it’s simply another factor worth taking into account alongside the weather, budget and the kind of break you’re looking for. Check whether your chosen destination requires EES before you travel.

“Like any new system, there’s always a settling-in period,” added Ricky. “The important thing is not to let the headlines put you off travelling. Millions of people are still enjoying holidays across Europe.

“If you know what to expect, allow a little extra time where needed and make sure your passport is up to date, the whole process should be straightforward.”