This is dodgy ground - you can pass an MOT with over 1.6mm over three quarters of the tyre, as Girlracer said, BUT...
Plod can still do you, as Im pretty sure they will say that that tyres illegal. I think its the case that you can pass an MOT like that then drive out and get 3points, £2.5k fine (max) for the same tyre... Stupid, yes, but then when have the laws in this country ever done anything good??
Im running a risk as mine are, literally, slick on the inside edge from running so much camber. Its not so bad as you cant really see it from outside, but the above pic shows how obvious it is to plod walking round your car! Dangerous...