Labour frontbenchers have defended their decision not to take part in Saturday's march by tens of thousands of people demanding a new Brexit vote.
The People's Vote campaign argues the public should have the final say on the terms of Britain's exit from the EU.
No senior Labour figures joined the demonstration and there were chants of "where's Jeremy Corbyn?"
Frontbenchers Nia Griffith and Rebecca Long-Bailey said Mr Corbyn had been visiting a refugee camp in Jordan.
Lib Dem Leader Sir Vince Cable and the Green Party's Caroline Lucas spoke at the event, which took place on the second anniversary of the EU referendum.
Backbencher David Lammy was the most senior Labour figure to address the crowds, which organisers have said numbered at least 100,000, athough several pro-EU Labour MPs, including Chris Leslie, Stella Creasey and Stephen Doughty took part in the march.
Ms Long-Bailey, the shadow business secretary, who was at a constituency event on Saturday, said: "I understand why people wanted to march yesterday - it is a highly emotive issue."
But, she told BBC Radio 5's Pienaar's Politics, a second referendum was not Labour policy and she had "significant concerns" about the idea.
She said the government would "hold the pen about what is contained within the referendum" and would, she claimed, be unlikely to offer staying in the EU as an option on the ballot paper.
She said another referendum "has the potential to divide the country yet again at a time when we should be bringing people together" and the priority now should be to get a Brexit deal that "suits our economy, protects jobs and puts a floor under existing rights and protections".
She denied the Labour leadership was out of step with party members, most of whom, according to a recent poll, are in favour of a second referendum.
"I wouldn't accept that," she told John Pienaar.
Labour's shadow defence secretary Nia Griffith said: "Of course people in a democratic country can do what they like and have marches and that's good and they should express their opinions."
But she said Labour had accepted the result of the June 2016 EU referendum and was now working for "a Brexit that works the best way possible for the economy and for jobs".
A People's Voice spokesman said they needed to get the Labour leadership on board to make a new referendum a "realistic proposition" and the party should "reflect the wishes of its own membership" on the issue.
Actor and Labour activist Sir Tony Robinson, a leading supporter of the People's Voice campaign who spoke at Saturday's rally in central London, accused Jeremy Corbyn of ignoring the views of the party's members and trying to shut down debate on a second referendum.
"He knows what he's doing and actually, objectively, what he is doing is supporting Theresa May in trying to shuffle through this awfully badly negotiated Brexit that we may be heading towards," he told Pienaar's Politics.
The actor, who has criticised Mr Corbyn in the past, said he wanted to see Brexit stopped but he was a "democrat" and thought the public deserved to be asked if the final deal was what they wanted.
He also claimed the public mood was shifting in favour of another referendum.
"I wouldn't say there was an avalanche yet," he told John Pienaar.
"One march alone isn't going to change the politics of the country... but I believe we are starting to see movement."