Originally Posted by Genius1

If you are flying into LHR in First, you could book a cheap same-day domestic flight from T5, and then would be able to access the Concorde Room before your domestic flight, if you really want to sample the Concorde Room.

I would argue that if it is to be your only time in the CCR, the relatively negligible cost of the domestic flight would be offset by the experience, especially if you allowed a good few hours to enjoy the CCR.