"I was wondering - is there anything legally that requires a vote from the HoC before committing British forces to action - or is it just a political backstop by the PM?"
without a written constitution he can do pretty much what he wants using the Crown prerogative - especially in times a danger
there is of course a move amongst the lawyers to say we have to have UN approval otherwise it might be a war crime
but in this day and age the PM wants to be able to say to them "well you damn well voted for it - it wasn't ALL my fault" when it goes pear-shaped .... as it always does