Brendan Chilton, Director of Labour Future UK has said that “people don’t want another vote” but that he supported the idea of people “marching in the street”.
Mr Chilton told talkRADIO’s Matthew Wright: “This country has got a long, proud history of people protesting and people marching in the street to push forward their cause.
“But I don’t think there is anywhere near the support in the country for a second referendum, which is what the march was calling for.”
He added: “The trend in opinion polls is that people don’t want another vote, they just want people to get on with it.”
He said: “I support them having the march but I don’t support the cause.
“I don’t think there is going to be a second referendum.”
'Put it on a red bus, Brexit sucks'
This comes after People’s Vote March organisers claim more than 600,000 anti-Brexit campaigners joined a march through London calling for a second EU referendum.
The People’s Vote March, also called the March for the Future set off from Park Lane at midday and finished at a rally in Parliament Square with speeches from Mayor of London Sadiq Khan and Celebrity Chef Delia Smith.
The People’s Vote campaign said its stewards estimated the crowd to be around 670,000 protesters.
It was originally predicted that the march would be attended by 100,000 protesters calling for a vote on the final Brexit deal.
Protesters could be heard chanting "Listen up Theresa May, the people want a final say" and "Put it on a red bus, Brexit sucks".
'They want to be heard'
Eloise Todd, the CEO of Best for Britain was also on the show.
She said: “For every hundred thousand people who marched, there were absolutely loads more at home that were with us in spirit on the streets.
“We got a hundred thousand people out in June and that skyrocketed to 700,000 on Saturday.
“Those people are motivated, they want to be heard.”
She added: “We haven’t even seen the final deal yet, but when it comes back we have to be able to have our final say.”
She said: “I think it is really important that the people in this country have a decision to make themselves about whether to accept the deal that the government is going to come back with. Or, whether to stay in on our current terms.”