Sakir Yildirim drove an ambulance from Bristol to Gaza in February 2009
Two men from Bristol were among those on board a convoy of boats which was intercepted by Israeli forces as it tried to approach Gaza.
Sakir Yildirim and Cliff Hanley were on the Mavi Marmara, which was carrying aid supplies, when it was boarded by armed commandos overnight.
At least 10 people were killed in the incident and many others injured.
The two men are members of the Palestine Solidarity Campaign (PSC) and had been raising money for the project.
Mr Yildirim and Mr Hanley, who have visited Gaza before, boarded the passenger ship Mavi Marmara earlier in the week.
Mr Yildirim, originally from Turkey and now living in the Fishponds area of Bristol, drove an ambulance to Gaza in February 2009.
Another Briton thought to be on board the boat is 37-year-old Alexandra Lort-Phillips.
Sally and Patrick Lort-Phillips, from West Lavington in Wiltshire, said they were concerned about their daughter, who is not affiliated to any group.
They described her as a "free spirit", adding that she was helping to deliver aid such as chemotherapy drugs. They said they were waiting to hear from the Foreign Office.
The six-ship flotilla, carrying 10,000 tonnes of aid, left the coast of Cyprus on Sunday and had been due to arrive in Gaza on Monday.