-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.
'Humanitarian catastrophe'
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.
