I thought it was a hard and fast rule (and in the T&Cs) that BA flights close 20 minutes prior to departure and that if you show up later than that BA have the right to offload you. What I question here is did the boarding pass say 12:15 or 12:10?

I certainly know that at AA we had the right to close a flight early if there was a good reason (i.e. incoming weather or long hold times at the arrival airport, most of the time at the Captain's request). This was sometimes essential to do if the flight was to leave and in order to facilitate connections.

Every BA BP I have got has always had T-20 as the closing time.

In any case you did not meet the security conformance time (which is 35 minutes before departure) which I believe is global (whether or not is enforced at certain airports is irrelevant).

In any case, I would never leave it that close for exactly this reason. Much better to get to the airport an hour before minimum in order to avoid this sort of scenario.

You can try for compensation but I do believe that T-20 minutes at the gate is in the T&Cs of the BA ticket, regardless of what the BP says.

Bad show by BA in any case for stating the wrong gate closing time. I have no objection to the flight leaving early within its allotted allowance.