The Fathers 4 Justice group clashed with police after a man involved in the flour attack on Tony Blair was held for breaching bail conditions.
There was a big police presence during the march
Ron Davis has been banned from the City of Westminster, after being accused of disrupting Prime Minister's Questions.
He arrived in a bus for a march on Friday which went into the area. As he was put into a police van, other protesters jostled with officers.
The march through central London was to highlight the rights of fathers.
A police spokesman confirmed a 48-year-old man had been arrested for breaching bail conditions and is still in custody.
Mr Davis, a father-of-two, faces trial for alleged threatening and abusive behaviour after an incident in which flour bombs were thrown at Tony Blair in the House of Commons.
Guy Harrison, who threw the flour bomb, has already been fined £600.
Matt O'Connor, founder of Fathers 4 Justice, spoke to the demonstrators, urging calm.
'Refuses to act'
He said: "I am very sad to tell you that the very brave Mr Ron Davis has been arrested by the police this morning.
"There will be a time and there will be a place where justice will be done and justice will be seen to be done."
Most of the 1,000 protesters were dressed in purple - the international colour of equality - while others wore outfits including Batman and Spiderman.
When the procession, which started at Lincoln's Inn Fields, passed the Family Division of the High Courts of Justice, protesters stopped and jeered.
Glen Poole, a spokesman for the group, addressed protesters at Trafalgar Square and said: "Every day 100 children are removed from their fathers' lives - this is a travesty that the government knows about but refuses to act upon.
"We are taking the problem to Tony Blair and telling him 'here is the problem and here is the solution'."
Fathers 4 Justice say that issues relating to children and the family are disjointed because they are spread over five government departments.
They have proposed that the government sets up a Department of Family Affairs and a Minister for Family Life.
When the group reached No 10 they were prevented from entering and handing in their petition which calls for better access to their children.
Officers said the group was unable to go in for security reasons, so the petition and several copies of their 'Blueprint in Family Law' document were passed through the gates.
As the protesters started to leave Downing Street, one of the members of the group, Paul Robinson, from Portsmouth, threw a couple of purple-coloured eggs at officers.
He was handcuffed by more than 10 officers before being bundled into a police van.
Gary Burch, another spokesman for Fathers 4 Justice said: "We see too much of politicians and so-called experts making decisions about how parents should parent their children.
"I think that power and trust should be put back into the hands of parents."