UK leader David Cameron 'deplores' Gaza aid ship deaths
Prime Minister David Cameron has told the Israeli PM he "deplored the heavy loss of life" caused during Israel's raid on aid ships bound for Gaza.
At least 10 people were killed, and a Briton injured, after commandos stormed a boat.
Mr Cameron spoke to Benjamin Netanyahu and is urging Israel to respond constructively to critics and lift the blockade on Gaza.
The UN Security Council has called for an immediate and impartial inquiry.
A Downing Street spokesman said: "The prime minister deplored the heavy loss of life off the coast of Gaza.
"He reiterated the UK's strong commitment to Israel's security, but urged Israel to respond constructively to legitimate criticism of its actions, and to do everything possible to avoid a repeat of this unacceptable situation."
Mr Cameron also stressed the need to urgently lift the three-year blockade - put in place to prevent arms smuggling to Gaza - and to allow full access for humanitarian aid, the spokesman said.
Deputy Prime Minister Nick Clegg said: "If we needed any confirmation about the unjustified and untenable blockade of Gaza, we have been reminded overnight of the need to lift this blockade.
"What is going on in Gaza is a humanitarian catastrophe. While of course Israel has every right to defend itself and its citizens from attack, we must now move towards lifting the blockade from Gaza as soon as possible."
Foreign Secretary William Hague suggested the best response would be for the international community to achieve "a durable resolution to the Gaza crisis".
Israeli ambassador in London Ron Prosor said the operation by its military forces was "not successful" and the loss of life was tragic.
But he said the passengers had tried to provoke them despite repeated warnings against breaking the blockade.
"The people on board the ships behaved appallingly. They used iron bars, metal pipes, knives with huge blades," he said.
Britain's ambassador to the UN from 1998 to 2003, Sir Jeremy Greenstock, told the BBC that Israel had to use "some kind of defence" to make sure weapons did not get into Gaza but "this was clearly not very well handled".
He said the time had come for serious international action to end Israel's blockade and what he called "the virtual starvation of Gaza".
The Foreign Office said it was not aware of any British nationals among the dead and confirmed an injured Briton had received medical treatment.
It is thought 28 UK nationals were travelling in the convoy, but contact with them has been difficult after Israel imposed an information blackout.
A number of families are facing a long and anxious wait for news of relatives.
Dr Khalid El-Awaisi said he was worried that his brother Ali, from Dundee, may have been injured.
Winnie Chambers is also waiting for contact from her sister, Theresa McDermott, from Edinburgh.
"The normal thing that happens is all communications are jammed and any communication devices are removed from the passengers," Ms Chambers told the BBC.
"We just cross our fingers and hope."
One man told the BBC his aunt was on the flotilla, but said he did not know where or how she was.
And Eleanor Lamb, of County Donegal in the Irish Republic, said she had been unable to get in touch with her son, Fiachra O'Luan, who was among the activists.
"He's courageous, and some might say foolish, but I just hope he will be OK," she told the BBC, through tears.
On Monday hundreds of protesters gathered near Downing Street in London to condemn the violence, and later moved on to the Israeli embassy in Kensington.
Other protests took place in Bristol and Manchester, where campaigners targeted a 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 military boarded it overnight in international waters and clashed with the 500 or so passengers, who were mostly Turkish.
The ship, a passenger ferry called Mavi Marmara, was one of three provided by Insani Yardim Vakfi (IHH), a Turkish aid organisation with links to the Turkish government.
The ships have now been escorted to the Israeli port of Ashdod and Israel says it will detain or deport the passengers from there.
Former foreign secretary David Miliband said it was right to condemn the death of innocent civilians and warned any inquiry should not be allowed to drag on for years.
He said Israel's blockade was "self-defeating" and was hampering the peace process.
"The particular circumstances of this case will have to be brought to the surface but the defence of a failed policy that is benefiting no-one - not the people of Gaza, not the people of Israel either - I think is badly flawed," 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".
Meanwhile, Israeli ambassador Mr 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.