The first boats were stopped on Wednesday about 70 nautical miles off the Gaza coast in international waters and others closer.
Swedish climate campaigner Greta Thunberg was among those detained
Israel has been policing this area but does not have jurisdiction there.
Israel said its navy told the boats to change course as they were “approaching an active combat zone and violating a lawful naval blockade”, while the GSF described the interceptions as “illegal”.
A UK Foreign Office spokesperson said: “We are very concerned about the situation with the Sumud flotilla, we are in touch with the families of a number of British nationals involved.
“We have been in contact with the Israeli authorities to make clear that we expect the situation to be resolved safely, in line with international law and with due respect for the rights of all those on board.”
Israel’s Foreign Ministry said those involved were being transferred to an Israeli port to be deported and all were “safe and in good health”.
