Assuming you are flying BA you will be able to use the Concorde room. If you are flying first on another oneworld carrier you will be able to use galleries first lounge. Either way they share the same showers which are between the two lounges (and don't let the seagull get out !)

If you are flying BA first you can try to book one of the cabanas in the Concorde room which would give you a private room and shower.