McCullum

Key was also a guest on the the TMS programme and he said England will make changes in the way they approach selection.

There had been a perception that the England Test team felt like a ‘closed shop’, particularly to players in county cricket who did not fit the aggressive Bazball style.

Key said the introduction of a “county insight group” to offer input into selection will attempt to formally rebuild relations with stakeholders, including directors of cricket, in the domestic game.

The 46-year-old former Kent captain also said England’s selection policy will become more cut-throat compared to the past when certain players have almost appeared undroppable.

“We’ve overvalued loyalty and overvalued having a settled team,” Key said.

“We thought what we wanted to do is make sure we have a team that is settled out there [in Australia], that we go out there and we’re not giving debuts to opening batters [during the Ashes] and stuff like that.

“But what that does is it creates an environment where there’s not enough consequence. We need to be more ruthless with our selection.”

McCullum is due to return to work towards the end of May as England gear up for a Test series against his native New Zealand which starts at Lord’s on 4 June.

However, Vaughan felt it would have been worthwhile McCullum spending time on the circuit during the early rounds of the County Championship – for good PR if nothing else.

“I’m a bit disappointed that he’s not coming a bit earlier,” Vaughan said.

“I think at this stage, when you’re trying to win back the fans, trying to win back a little bit of the game, if I was Brendon McCullum, I’d come a few weeks earlier, get seen around the counties.

“I’d go and talk to a few coaches, go and speak to a few umpires, get seen out and about just for the optics. Because at this stage he needs the fans, and he needs the game to kind of get behind his philosophy a little bit more.”

You can watch the full TMS debate over the post-Ashes review on BBC iPlayer or download it as a podcast.

“I’m enjoying the role across all formats and I’d love to carry that on,” added McCullum.

“It’s been an absolute privilege to be in this position over the past three and a half years. I feel like we’ve made some significant improvements across the various formats.

“Yes, we’ve missed some opportunities, but I think this team has a real opportunity over the coming years to continue to improve and hopefully finish what we started. I’d love to be a part of that.”

Key backed McCullum during the Ashes, but neither ECB chief executive Richard Gould nor chair Richard Thompson have publicly spoken on his future.

At the end of the Ashes, McCullum also received support from Test skipper Ben Stokes, while the relationship between McCullum and Brook has blossomed during the T20 World Cup.

Asked after the semi-final defeat if McCullum should stay in charge, Brook said: “125%. I’ve said plenty of times he’s the best coach I’ve ever had.

“The way he speaks to everybody, he’s got an aura in the dressing room, and everybody looks up to him. The things he’s done over the four years since he took over has changed English cricket for hopefully the best.

“Our partnership has been good throughout the competition and since I’ve taken over. Long may it continue.”

Failures in away Ashes tours have often signalled change in the management of England teams.

Speaking on Sky Sports, former England captain Nasser Hussain said the ECB has to guard against repeating the mistakes of the past, while not ignoring the failures of this latest defeat in Australia.

“What you have to get away from is going to the Ashes, you lose, you get rid of the coach and captain, and you start all over again. I’m never a fan of that,” said Hussain.

“But I’m also not keen on, a couple of months later, forgetting what happened in the Ashes, and how poor England were on and off the field – all the mistakes that were made.

“There is a feeling Brook and McCullum are aligned, but there is a suggestion there was a divergence during the Ashes and that is a concern.

“They’ve made good decisions in the white-ball game that they didn’t in the Ashes. They missed an opportunity there and you can’t just brush over that.”