Andrew Hill and aid worker Dylan Healy are understood to be under investigation as mercenaries.
Suspended Tory MP Chris Pincher says he hopes to return to constituency duties "as soon as possible".
More than a million people packed London for Pride's 50th anniversary, the mayor's office says.
BA and Heathrow say the move will help minimise disruption for passengers during the peak season.
Mason McKenzie has been having gruelling treatment since he was diagnosed with leukaemia.