When Moneybiker asked a similar question on this thread
http://www.uk-muscle.co.uk/general-conversation/230913-mini-cooper-oil-light.html
several people said that they'd come across the same problem due to nothing more than a faulty (and cheap to replace) oil pressure sensor switch. So that's certainly one possibility to consider (as you already seem to be doing anyway).
However Moneybiker had already changed the switch and the fault was eventually traced to a 'blocked pipe'. Either way it doesn't sound too expensive to fix.
Is it OK to drive? Well, I'd probably risk it but it does rather depend upon the cause. If it's just a faulty sensor then the oil pressure is actually OK, so you can obviously drive the car without any problems but a different cause could mean that the pressure really is too low, so driving it might be unwise.