Sound HKG advice from
ba97.com. If you want to get a decent nights sleep on the plane, a slap buffet feast in the Wing and a glass of 'poo on the plane will see you arrive at LHR is style. It is a 5-10 min walk from the CX lounge to the BA gates. You can go the scenic way through the shopping - perhaps with a quick stop at the Shanghai Tang store ^ - or just walk out of the lounge entrance, past where the pax emerge from security and keep walking along. There is a little passage 'behind' the restaurant area that will bring out near a lift down to the gates. The misanthrop's way of getting there.
The T1 arrivals lounge breakfast is every bit as good as the T4 effort.
I don't think there is a 'fancy' shower in T1, but could well be proven wrong.