Police said 10,000 people had gathered in Trafalgar Square before marching to Hyde Park. No arrests had been made.
The march is being led by the Muslim Action Committee – an umbrella body for mosques and community groups.
It is the third consecutive weekend of demonstrations over the cartoons, which have prompted violent protests around the world since publication in Denmark.
The committee was also due to launch a charter supporting a ban on religious discrimination after the march.
Organisers said there were 400 stewards to control the demonstration.
Ishmaeel Haneef, from the committee, said the demonstrations were continuing because “the provocations have not stopped”.
“These things are still being republished across the world,” he said, using the example of an Italian minister wearing a T-shirt depicting the cartoons.
He said the way to “get back to being a civilised world” was to “give the copyright [of the cartoons] over to the Muslim community”.
Protests against the cartoons, first printed in Denmark, have taken place in Muslim countries across the world.
Outbreaks of violence across Pakistan have prompted Denmark to temporarily close its embassy in Islamabad.
Last week protesters waved banners calling for unity against Islamophobia in a peaceful demonstration.
Guest speakers at that event included Respect MP George Galloway and Ben Kent, friend of British hostage Norman Kember.
The Muslim Council of Britain along with the Muslim Association of Britain and a number of Christian groups, peace organisations and the Mayor of London helped organise that protest.
The event was intended to highlight the opinions of moderate Muslims after demonstrators earlier this month carried placards threatening violence through the capital.
Among the images which have sparked outcry is one of Muhammad with a bomb-shaped turban on his head.
Newspapers in Spain, Italy, Germany and France reprinted the material.