Foreign Secretary William Hague has said he "deplores the loss of life" caused during the Israeli navy's interception of a flotilla of aid.
At least nine people were reportedly killed after commandos stormed a ship destined for the Gaza Strip, and a Briton was injured.
Israel says its soldiers were shot at and attacked; activists say Israeli troops came on board shooting.
Mr Hague called for limits on aid for Gaza to be lifted.
Consular access has been granted to the injured Briton and access to other Britons on the boats was being sought, Mr Hague told the BBC.
The exact number of UK nationals on board the vessel is not yet known, but reports are coming in to the BBC that at least five Britons may be on the ship.
EU ambassadors from 27 nations, including Britain, are holding emergency talks to discuss the deaths.
Meanwhile, hundreds of protesters gathered near Downing Street in London to condemn the violence, and later moved on to the Israeli embassy in Kensington.
Activists blocked Whitehall shouting "Free Palestine" and carrying flags and banners with slogans including "Stop Israel's War Crimes in Gaza" and "End the Criminal Siege of Gaza".
The BBC's Louise Hubball said around 1,500 people were gathered at the embassy and that there had been "angry" scenes.
She said the protesters - who included families with small children and some Jewish demonstrators - were calling for the Israeli ambassador to be ejected from the UK and for the British ambassador in Tel Aviv to be recalled.
Kate Hudson, chairman of the Campaign for Nuclear Disarmament (CND), told the gathering it was "devastating and deplorable that the Israeli forces have attacked civilians".
Other protests have taken place in Bristol and Manchester, where campaigners targeted the BBC building, smashing doors and placing a Palestinian flag on the roof.
The ship, carrying 10,000 tons of aid, including cement and building materials that Israel bans from Gaza, left the coast of Cyprus on Sunday.
It had been due to arrive in Gaza on Monday, but Israeli armed forces boarded it overnight in international waters and clashed with the 500 or so people onboard.
The ship, a passenger ferry called Mavi Marmara, was one of three ships provided by Insani Yardim Vakfi (IHH), a Turkish aid organisation with links to the Turkish government.
Most of the passengers were Turkish and at least two journalists are known to be on board.
Other vessels in the six-ship flotilla were organised by the Free Gaza Movement, an international coalition of activist groups
Israel says the flotilla was breaking a blockade put in force to prevent arms smuggling to Gaza and it had repeatedly said the boats would not be allowed to reach the territory.
Israeli Prime Minister Benjamin Netanyahu, who is in Canada, has cancelled a scheduled visit to Washington on Tuesday to return to Israel, officials said.
Earlier, he expressed his "full backing" for the military involved in the raid, his office said.
UN chief Ban Ki-moon and the European Union have called for an inquiry to establish what happened.
Mr Hague joined the widespread condemnation of the violence on Monday, saying there was a need for Israel "to act with restraint and in line with international obligations".
"It will be important to establish the facts about this incident, and especially whether enough was done to prevent deaths and injuries," he said.
He suggested the best response would be for the international community to achieve "a durable resolution to the Gaza crisis".
"I call on the government of Israel to open the crossings to allow unfettered access for aid to Gaza, and address the serious concerns about the deterioration in the humanitarian and economic situation and about the effect on a generation of young Palestinians," he said.
He added that the British embassy was in contact with the Israeli government and officials were asking for more information and urgent access to any UK nationals involved.
"We don't know for certain yet about any deaths, we know there may have been UK nationals who have been detained, and we are seeking consular access to them," he told the BBC later.
One man told the BBC his aunt was on the flotilla, but they did not know where or how she was.
"Up until yesterday she constantly kept us up to date on the course of events and how she is keeping. Since this attack on the ship we haven't heard anything from her and we are sincerely quite concerned about her well-being and her safe keeping," he said.
Former Prime Minister Tony Blair, who is the Quartet Representative in the Middle East, expressed his "deep regret and shock at the tragic loss of life".
"We need a different and better way of helping the people of Gaza and avoiding the hardship and tragedy that is inherent in the present situation," he added.
Scotland's deputy First Minister Nicola Sturgeon asked the Israeli government for immediate reassurances about the fate of a number of Scots on board the flotilla.
Former Liberal Democrat leader Sir Menzies Campbell said only an "independent, international inquiry" would do to find out what precisely happened.
Green Party MP Caroline Lucas described the attack as a serious infringement of the principles of international law and called on the UK government, and the EU, to apply pressure to lift the blockade.
Islington North MP Jeremy Corbyn called for "appropriate and immediate" sanctions against Israel for "clearly illegal acts".
Meanwhile, the Israeli ambassador Ron Prosor has withdrawn from his scheduled appearance at the Hay Festival of Literature on Tuesday.
In 2007, Israel and Egypt tightened a blockade of Gaza after the Islamist movement Hamas took power there.
Israel says it allows about 15,000 tonnes of humanitarian aid into Gaza every week, but the United Nations says that is less than a quarter of what is needed.