John Woodcock is calling on Rishi Sunak and Sir Keir Starmer to bar their MPs and councillors from interacting with groups like the Palestine Solidarity Campaign until they “cut the hate”.
They should also sever ties with eco-zealots like Extinction Rebellion and Just Stop Oil who use “illegal” tactics, he said.
The Palestine Solidarity Campaign has organised protests about the war in Gaza across the country.
But these have been marred by anti Jew hate and chants of “from the river to the sea” – which can be seen as genocidal by calling for Israel to be wiped out.
Labour MPs with ties to the PSC include John McDonnell, Richard Burgon, Apsana Begum, Beth Winter and Afzal Khan.
Former Labour leader Jeremy Corbyn is a patron.
Writing in today’s Sun on Sunday, Mr Woodcock – whose formal title is Lord Walney – said: “It is not on to cause mayhem on our streets and menace elected representatives here in the UK so they live in fear.
“But we need action on this thuggery that threatens to undermine our proud democracy, not just words.
“Rishi and Keir should instruct their MPs and councillors not to engage with anyone from the PSC until they get they get their house in order and cut the hate from their marches.
The same goes for hardline environmental groups like Extinction Rebellion and Just Stop Oil whose tactics can be to create illegal disruption to get noticed and get their way.
If you threaten MPs and break the law try to get your way, you should never be invited into the room to express your views.
“For too long, too many who have the privilege of making our laws have seen extreme, highly disruptive protests as a vital expression of democracy rather than the truth – that they are a threat to it.
“It is time to reset the balance and put our prized liberal democracy first.
His call is one of a series of recommendations contained in his report on tackling political violence in Britain, which is being passed to the PM shortly.
In a dramatic speech on Friday evening, the PM told Brits there are “forces” which are ready to tear the country by spreading the “poison” of extremism.
He singled out Islamist extremists and the far right desperate to set “Briton against Briton” in an address outside No10.
Labour leader Sir Keir backed Mr Sunak saying he was right to condemn “unacceptable and intimidatory” behaviour.
Sir Keir was abused in the street this week with protesters screaming “you’re not human” and calling him “Sir Kid Starver”.
And PSC activists protested outside Barclays branches yesterday telling customers to close their accounts, claiming the bank is linked to arms companies supplying Israel.