Yep the Pier at Gate 63 is great. Go there for nice food and a decent bar. The BA flight will probably be form gate 12-15 or 1-4 so the wing would be good for that. However, if you want a shower use the Pier. I find the loos in the wing to be too dark. I never think they are that well stocked with hand-towels etc.
Both are light years ahead of the Elemis (AKA I'll give it a miss) spa (ha ha) in LHR T5