Mark,
Your wife should have to hand every bit of information she can think of relating to exiting and flying.
Did you pay for the flight directly from your UK debit/credit card?
If yes then I strongly suggest she has a photocopy of that card and you have cleared it with the carrier. Some carriers are OK and some can give a hard time.
I can't recall which airline you're using or even which ones are most difficult but I'm sure others can input valuable information.
Please follow this up urgently.