There are may ways that ID can be checked. If you have a bank statement this is normally a form of identification if it is registered at the same address as your main residence, you may be on the electoral roll, you may be in receipt of certain government benefits.
If you have an up to date (within the last 3 months) document of any one of these items above then you can either present this in person to the bank or even get your local police station, solicitor or accountant or even your local MP to certify the document against your own identity and pass this on to the lender.
But to tell you the truth, normally at this stage of an application it is the financial underwriting that the lenders will be looking at as the identity part of it is usually done through credit reference agencies and entry on the electoral roll and other means on the intial approach to the lender for acceptance. If you say the finances aren't a problem then its just a matter of waiting butdo not be afraid to contact your lender or broker to get an update on the application. Call 20 times in a day...it won't impact on your application but it will get their *** in gear!
Big Brother is watching....its pretty hard to get away fromk him nowadays even if you don't drive or leave the country at any point :)