The oil service warning light on the BMW was still on after the last oil service, so I looked around for how to reset it. Lots of advice on the internet, but mainly involving special tools (aka paperclips) and dodgy shorting-out of pins in the diagnostic port.
There's also talk of holding down the trip reset button whilst turning the ignition key to the first position, then releasing and pressing and holding the button again. But there IS no ignition key in the recent BMWs..
The answer turned out to be a bit more easily guessed (after a bit of trial and error). When you start the engine, the oil service warning shows on the dashboard, at which point you just press the BC button on the end of the indicator stalk (which is how you access most of the diagnostics anyway). The word "reset" appears, and another click and hold on the BC button makes it show "resetting" (and a little clock icon so you know it's busy). And that's it.
Put away the paperclip.