OneBeck: I tried that. Several times. Nada....
<rant>So the only solution appears to be "buy a wired keyboard to use for pairing the bluetooth keyboard"!. Thats bonkers!
Do I really have to be locked out of my mac until I can get a wired keyboard? Whats the point of a wireless keyboard then? I thought Apple stuff "just worked", which is why I paid a 50% price premium. </rant>
Seriously though, is there really no other way to get into my mac mini (accounts are password protected, natch)? There are no other keyboards in the house (apart from the built-in one on my macbook pro and the virtual one on our iPads)
Edit:
Further googling revealed this promising article: http://www.cultofmac.com/247979/whoops-reconnect-your-bluetooth-keyboard-and-mac -after-logging-out-os-x-tips/
But, before I got that far, I tried turning off bluetooth on my iPad (despite not recalling pairing the keyboard with it in the past) and then found the keyboard magically "just worked".
Case solved.
Moral: don't try to solve problems when you are cross!!