Leading speeches in Parliament Square, Delia said people were not fully informed when they voted but now understood "the dire consequences". One placard hoisted aloft in the crowd said: '56% say protect Good Friday'.
Mr Wilson was speaking at Saturday's mass rally in support of the "people's vote".
Civil servants have reportedly begun contingency planning for a second Brexit referendum amid fears Theresa May is unable to get parliament to back a deal.
Elsewhere, Crazy Rich Asians and Humans star Gemma Chan tweeted a snap of herself with a banner reading: "Even Baldrick had a f****** plan".
Thousands of people filled the streets, some were singing, others were playing instruments, while many plastic whistles blared out.
The electorate voted on in 2016 to Leave the European Union with no ifs nor buts.
Britain is scheduled to leave the European Union on March 29, but negotiations have been plagued by disagreements.
Earlier, Farage, the vice chairman of the Leave Means Leave, the pro-Brexit pressure group responsible for organising the rally in Harrogate, had tried to get into Bettys but was faced with a lengthy queue.
"How would anyone have known what type of Brexit we were going to have?" he said.
Beaconsfield's Dominic Grieve for instance - the former Attorney General - is quoted as saying "If you think the future of our country matters and that we should prevent a very bad outcome. please participate in the People's Vote march".More news: Italian finance minister Giovanni Tria faces European Union scrutiny on budget
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Vix Lowthion travelled up to London with her family...
London Mayor Sadiq Khan is among some of the prominent politicians to throw their support behind the People's Vote campaign, which is demanding a vote on the final deal with the European Union in the form a fresh referendum.
In a direct appeal to the public, she has acknowledged that many people are tiring of the negotiations that have felt "never-ending" and said she sometimes feels the same.
Mayor Sadiq Khan said: "What's really important is that those that say that a public vote is undemocratic, is unpatriotic, realise that in fact, the exact opposite is the truth".
Numerous posters featured variations on the famous "I have a cunning plan" line from the popular 1980s British comedy "Black Adder".
"It is a losers' vote by those who don't understand why 17.4 million people up and down the country voted to leave".
Most people who voted Leave in 2016 did not do so because they were bigoted, or because they were stupid, but because it felt like the opportunity to give the political class a punch on the nose.
"This feels like a party", said Liverpool university student Lucy Dogget as she squeezed past a volunteer dishing out bowls of beans on a leafy square facing Westminster Palace.
The 54-year-old said: "The will of the people doesn't have to stand still, it's not an immovable thing that is fixed. I'm going to be poorer and not have the same career opportunities".
Joe Trickey, from Croydon, was celebrating his 83rd birthday at the march.
He also added that he "would not vote in a second referendum".