Protests have been mainly peaceful in London
Thousands of protesters gathered in central London to take part in May Day demonstrations have been asked to disperse by police.
A minor clash between protesters and police took place early in the day, but police said the rallies had been "relatively peaceful".
Seven arrests had been made by mid-afternoon for minor public disorder offences.
One male police officer was treated in hospital after being hit by a missile, but was not seriously hurt and was later discharged.
More than 400 people were still demonstrating in Trafalgar Sqaure, central London, at 1920 BST.
The protesters were split into three groups, with police in riot gear surrounding the main group.
Streets around the protest sites had been cordoned off, but police could not say when they would be re-opened.
Police had asked demonstrators to disperse by 1905 BST, but hundreds were continuing their protests after the deadline had expired.
Earlier, an official TUC march of 1,500 people had gathered at Trafalgar Square.
Some demonstrators had also marched from Trafalgar Square to Parliament Square, staging a protest outside Downing Street en route.
Deputy Assistant Commissioner Andy Trotter said there still "a bit of pushing and shoving" on Whitehall, but the day had been quiet.
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.
Previous May Days have seen riots and mass arrests in central London, with offices and businesses being attacked. Last year 54 arrests took place.
Mr Trotter said police were still on alert as trouble during previous May Day protests had not broken out until the evening.
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 had been demonstrating outside Lockheed Martin in High Holborn, when trouble erupted at around 1430 BST.
Protesters charged police officers who were not wearing riot gear, before being pushed back by police reinforcements.
Some demonstrators unfurled flags and staged a sit-down protest in the middle of the road.
They were contained within heavy police lines, bringing traffic in the area to a standstill.
Police have been issued special powers that allow them to contain protesters until they agree to disperse from the area on a route defined by police.
Police had filmed some protesters, many of whom were wearing masks.
A separate group of approximately 30 people protested in Oxford Street and Oxford Circus, watched by police.
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.
May Day map of London
Events, locations and times
Earlier about 1,000 protesters ran and walked from The Strand to Piccadilly Circus, escorted by police on foot.
After heading off into a narrow Soho street, they changed their minds and marched back to Trafalgar Square with no sign of trouble, joining the TUC gathering.
The first London demonstration saw no trouble outside the Dolce and Gabbana shop on Old Bond St, where anti-fur protesters were outnumbered by members of the media.
Police forces spent months preparing road closures and training in riot control and a total of 4,000 officers were expected to be involved in London. Scotland Yard has cancelled all leave.