Riot police surround protesters in Trafalgar Square
Police have criticised a minority of May Day protesters who they say attempted to wreak havoc in London amid peaceful demonstrations across the UK.
Sporadic protests in central London had dispersed by late on Thursday night.
Scotland Yard said the annual protests had passed off peacefully and were for the most part good-humoured.
There were 32 arrests for public order offences with one person charged with criminal damage and possession of a weapon.
Demonstrators said they had gathered to protest not just against the war with Iraq, but also against capitalism.
One male police officer was treated in hospital after being hit by a missile, but was not seriously hurt and was later discharged.
Thousands of anti-capitalist, anti-war and anarchist groups also took part in May Day events in other major UK cities including Liverpool, Glasgow, Edinburgh, Manchester, Leicester and Bradford.
For most of the day police outnumbered protesters in London with 4,000 officers on duty.
A hard core of protesters stayed on until the evening in Trafalgar Square where there were scuffles and minor clashes.
Deputy Assistant Commissioner Andy Trotter said: "It is a shame and deeply disappointing that a minority of people feel the need to use the day as a reason to cause serve disruption and disorder.
"It is unacceptable that the police should have to marshal a small number who pay no heed to any instructions or warnings".
Earlier an official TUC march and rally attracted about 3,000 people who gathered at Trafalgar Square.
Mr Trotter praised this demonstration as being an example of how a protest should be carried out.
Arms manufacturers and oil companies were among the targets of the demonstrations.
Some demonstrators had also marched from Trafalgar Square to Parliament Square, staging a protest outside Downing Street en route.
Guy Taylor, of Globalise Resistance, one
of the groups that organised the demonstrations, said: "People see the common strands between all the different
campaigns," he said.
"It's not just war, it's the system that breeds war, it's
May Day map of London
Events, locations and times
Margaret Jones said she was protesting against Prime Minister Tony Blair's decision to commit Britain to the
"illegal" invasion of Iraq.
The 65-year-old retired secretary waved a banner saying: "Welfare not warfare".
Previous May Days have seen riots and mass arrests in central London, with offices and businesses being attacked. Last year 54 arrests took place.
Earlier in the day about 20 campaigners attempted to break through police lines outside the central London headquarters of an arms manufacturer.
About 200 people demonstrated outside Lockheed Martin in High Holborn.
Protesters charged police officers who were not wearing riot gear, before being pushed back by police reinforcements.
The Charm protest - a cycle ride by about 150 members of the Critical Mass organisation - stopped for a sit-down protest in St James's Park, after travelling from Waterloo Bridge.