They are due to march through central London and will end with a rally in Parliament Square.
The dogs and their owners gathered in Parliament Square after marching through central London.
Speakers due to address the rally include actor Peter Egan and Stella Creasy, Labour MP for Walthamstow.
Tiffany Haynes, 32, a dog walker from London, took Welsh Collie Megan with her to the march.
She said: “I think this is a nice idea for a protest, it’s a clever way of doing it because dogs make light of politics and bring people together.
“People can relate to each other more with their dogs.”
Political writer Alastair Campbell brought his five-month-old Cavalier King Charles Spaniel puppy Skye to the march.
Mr Campbell, 61, said it was her “first-ever rally” and he plans to bring her to the “People’s Vote March” on October 20.
He said: “It’s a very British sort of thing - people love their animals and there are serious animal welfare concerns with Brexit, but the reason I wanted to come is that I do think the people’s vote has got to happen.
“The Brexit that is now on offer is so far removed from anything that was promised and far from it being undemocratic to have a second vote, I think it’s undemocratic not to.”
He said that politicians were “scared” of having a people’s vote on the outcome of Brexit negotiations.
He said: “They know the will of the people is changing, if Theresa May can’t even unite her party around this vision of Brexit, how is she going to unite the country?”
David Elkan, the founder of Wooferendum, started the campaign a year ago as a “secret protest” by taking photographs of dogs with campaign signs and putting them up in public places.
He said: “So many people don’t speak out when it’s a tough, dry topic, but if people don’t [speak out] politicians don’t hear it.
“The reaction I got from dog owners was so enthusiastic and it was like feelings were pouring out through the dogs.”
Mr Elkan, 45, who isn’t a dog owner himself, said the idea for the “Wooferendum March” was initially thought of as “bonkers”, but was well received.
He said: “It’s brought people together who would have never gone on a march but do want to make their feelings clear with their dogs.”