(BBC) Demonstrators at the “March for Europe” rally, which was organised on social media, are holding placards saying “Bremain” and “We Love EU”.
Protester Mark Thomas said the referendum campaign – which resulted in the UK voting by 52% to Leave – had not been fought “on a level playing field”.
But critics said that those who lost the vote were “having a tantrum”.
Demonstrators gathered around Park Lane before setting off for Parliament Square.
March organiser Keiran MacDermott said protesters hoped to stop the government from triggering Article 50, which begins the formal process of the UK’s withdrawal from the EU.
‘Outraged’
Among the crowd were Bill Baker, 59, and his daughter Jess Baker, 22, from Islington, north London, who had made a banner for the march which read: “I will always love EU.”
Ms Baker said: “We didn’t want to leave, but if you respect the decision of the referendum – which we should – we still want Britain to be EU orientated, outward looking and inclusive.”
Fellow protester Mark Thomas said the referendum campaign “was full of misinformation and people need to do something with their frustration”.
At the scene
By Martha Buckley, BBC News
There is no official turn-out figure for this protest but there must be several thousand at least on the streets around Hyde Park corner.
There are whole families here as well as the young, the middle-aged, the elderly, British, European, Londoners, as well as those who have travelled from further afield.
The protest has been organised hastily, with a call put out on social media less than a week ago. Today many of those who spent the week sharing anti-Brexit memes online have turned up to voice their concerns in person.
There are placards, signs and banners aplenty expressing anger and resentment at the way the Leave campaign was conducted but also frustration at what’s seen as a lack of clear leadership in the aftermath of the vote.
There is barely an organiser in sight and police presence is very low-key – but this outpouring of feeling is also quintessentially British: Calm, polite and orderly.
Laura Honickberg, 33, from London, said she was concerned that the vote would lead to a rise in violence and hate crime.
“I’m Jewish and I find the rise of nationalism and hate crime in Europe deeply concerning,” she told the BBC.
She added that she felt the Leave campaign “was based on lies, about money that was going to go to the NHS and now isn’t, about what’s going to happen to the economy. These are things that are going to directly impact me.”
The protest drew some criticism on social media under the #MarchforEurope hashtag, with posts pointing out that 17 million people had voted in support of Leave.
One user on Twitter accused the march of being “pathetic”, adding: “Just people having a tantrum about the fact they didn’t win.”
Others shared GIFs of toddlers having tantrums and compared them to those taking part.
The Metropolitan Police said there would be officers at the event to provide “flexible and appropriate” policing.
Meanwhile, Conservative MPs have been lining up behind candidates to replace David Cameron as the next prime minister and leader of the party.
Former Conservative leader Iain Duncan Smith came out in support of Andrea Leadsom. They campaigned together for the UK to leave the EU, and Mr Duncan Smith said she was the “right person to lead” in the forthcoming negotiations.
Mrs Leadsom has said the new PM must be a Leave supporter – which would rule out frontrunner Theresa May.
On Thursday, Justice Secretary Michael Gove, one of the most prominent figures in the Leave campaign, announced he was running.
He pledged to leave the EU’s single market, make public services “more human” and strengthen the United Kingdom, saying the country’s “best days lie ahead”.
The other candidates to replace David Cameron are Stephen Crabb, and Liam Fox.
