Hermia is correct, the whole reason a bank will lend 3 1/2 times a salary is because that's whats affordable for people to pay back. Self Cert is for people who genuinely cannot prove they earn a regular amount, even if they make a false claim they could be prosecuted.
Having said that most lenders don't give a toss as long as your paying up each month, Buenchico is correct in the fact they would be legally obliged to notify the Police if they found out but they are unlikely to check unless it was going to effect them.
However.... last year there was a change in the mortgage law, it used to be the case that the person getting the mortgage was liable if later found out, now the situation is that the lender is also liable and therefore more likely to check up in the first place.
I suppose it comes down to a moral issue, if not a strong legal one. If I killed 10 tramps and nobody cared are noticed would that be OK? An extreme example but same principle.