I dont think anyone has mentioned this yet (aside from the poster above who beat me to it )- you will also have access to the Arrivals lounge in Terminal 5 which does a better breakfast than the Galleries Club lounge.

To get there does mean entering the UK but you will have access to the fast track immigration channel as you're in J. Any hold baggage will be checked right through to Jakarta, so no worries there.

I'd do that so you can freshen up (J lounges airside have showers too) then decide if you want to head into London for a couple of hours.

If not, just head back through security and hit the lounge again - £125 for a day room at the sofitel seems quite punchy, mind you.

I think I'm right in saying that as the early flight to HKG is an A380, you will leave from the C gates. The lounge at the B gates is often a lot quieter than the main terminal, so it may be a better place to hole up for a few hours.