And to complete the story, Garuda on check-in gave us tags all the way to LHR with appropriate transfer labels on the bags.
The BA agent doing a passport check at Singapore (we left airside to visit the Jewel) searched for the tags and made sure the bags were indeed on the right flight.

Amusing postscript; the bags had a yellow priority tag (Garuda uses this for its business class PAX) and so despite not travelling in F from SIN to LHR the bags ended up being taken off the line and put in the little roped off area for first passenger's bags in T5 baggage reclaim...