In LHR I believe you will be flying out of T1 (NRt flights used to depart from T4).

There are many posts here which talk about the MB Spa - T4 has it and I think T1 has one now too.

I also flew into NRT on BA but connected to CX to HKG. Not sure about BA/QF lounges, but the CX lounge was pretty good - some food and open bar, free Internet terminals, etc... Not sure about showers but I am sure they can accomodate. Ofcourse you can only use CX lounge if you're OW Sapphire or Emerald (since you're flying with OW airlines).

QF uses the JAL lounge in NRT - I would guess it would have to be pretty good since it's their home airport. But the QF site doesn't mention showers etc.. there..but see here:

http://www.jal.co.jp/en/lounge/nrt/nrt.html