Most illegal immigrants enter the UK conventionally and then do not leave when visas expire. There are certainly some hiding in the back of lorries etc - but it's not the majority.

So fingerprinting them means for sure that we know they came in. I'm not sure what that achieves though?

No, but it would prevent people giving false information when suspected of overstaying their visa. It would also enable people to be identifed if they try and make several attempts to enter the UK via different methods. EG once legitimately, and once caught under a lorry.