Israel has released and is in the process of deporting the remaining British activists arrested in its raid on a Gaza-bound aid convoy.
Foreign Secretary William Hague has said 37 British nationals, including 11 with dual nationality, were involved. Five have already been deported.
He said he was concerned at the raid taking place in international waters.
Prime Minister David Cameron condemned it as "completely unacceptable", saying he deplored the loss of life.
In his first Commons question time, he said everything should be done to prevent it happening again.
Israel is in the process of deporting nearly all of the 682 detainees.
The remaining Britons are currently either on flights or awaiting planes at Ben Gurion airport, Tel Aviv, the BBC understands.
Consular staff are ready to provide assistance both at the airport and in Turkey, the Foreign Office has said.
None of the Britons was currently believed to have been involved in any violence against Israeli servicemen who boarded the ships, Mr Hague told MPs.
Nine activists died when Israeli commandos boarded the six-ship convoy on Monday, prompting increased international pressure on Israel to lift its blockade of the Gaza Strip.
Mr Cameron told the Commons: "We should do everything we can to make sure this doesn't happen again.
"Friends of Israel - and I count myself a friend of Israel - should be saying to the Israelis that the blockade actually strengthens Hamas's grip on the economy and on Gaza.
"And it's in their own interests to lift it and allow these vital supplies to get through."
He added: "We should do everything we can through the UN, where resolution 1860 is absolutely clear about the need to end the blockade and to open up Gaza."
Acting Labour leader Harriet Harman called for the blockade to end and added: "This is a tragic loss of life which has angered the Palestinians and dismayed friends of Israel too."
Earlier Deputy Prime Minister Nick Clegg questioned whether it was in Israel's interest to "confine" so many people.
He said the blockade was a "humanitarian catastrophe" and neither sustainable nor tenable "in its present form".
Activist Hasan Nowarah, from Glasgow, said he was the first to be sent home because he had injured his leg during the raid.
Originally from Ramallah, he runs the Glasgow-based group Justice for Palestine and was in one of the smaller ships in the convoy.
"The minute they landed into our vessels they were shooting and killing innocent people," he told the BBC.
"We were in the international water, we were not a threat of any kind to the Israeli civilan, government or army."
He said an Israeli soldier hit him on his back and leg with his gun.
"We were unarmed, all we had were the chairs and tables we were sitting on to defend ourselves from the Israeli guns," he said.
Friends and relatives of those caught up in the raid have complained about the lack of communication.
Rachel Bridgeland, whose partner Peter Venner, 63, from Ryde, Isle of Wight, was on the convoy, said more pressure should be applied on Israel.
She said: "It's absolutely terrible not knowing what has happened to him and it's terrible that the British government hasn't done more but they don't want to fall out with Israel."
Sarah Colborne, campaign and operations director for the Palestine Solidarity Campaign (PSC), was also among those being held.
PSC general secretary Betty Hunter said: "Those held illegally by the Israeli government have committed no crime, they have simply attempted to avert a humanitarian disaster by bringing much-needed medical supplies into Gaza."
Israel maintains the commandos were attacked first, saying its soldiers were attacked with "knives, clubs and other weapons" when they landed on the Mavi Marmara and had opened fire in self-defence.
Video clips show activists wielding a baseball bat and other objects, although some witnesses say they were acting in self-defence.
Former prime minister Tony Blair, a Middle East envoy, told the BBC the search for peace must continue, despite events.
He said: "We have got to continue the proximity talks that we want to turn into full blown direct negotiations over all the core issues between the Israelis and the Palestinians."
He added any internationally-led inquiry must be "full and fair and impartial".