Thanks guys,

the transfer was painless, but not well-marked...and ground staff were clueless...

So here's what works:
when you get off the inbound, look for an escalator going down with signs for Terminal 2A. (Don't keep going with the crowd on the arrival level as that goes to Immigration)

Take the escalator down, and there is a small connections desk, I was asked to pick up a phone and call a BA agent to confirm I was checked in etc. There is a small security checkpoint after which I took escalators back up to the gates/AC