They shortened the opening times, as it reflected the changes to the timings of the majority of flights.

They should let you in at 12:20, but they will normally inform you of a cut off point to leave. (It used to be 15-30 mins after official closing time) They may well have already closed off food orders and shower access by then, but you may get lucky.

Agree with OCC about London hotel times. I've not normally had too much of an issue getting earlier room access at most hotels if you request it in advance. It looks like you won't be at your hotel until early afternoon anyway, so not an unreasonably early request for a room.