I am sure somebody will post the reference, but last time this came up you were allowed to in effect write your own logbook, and then you swear an oath to certify it.
The signatures, should you actually ever need them, should be retrievable from the schools in question (if in the UK) because they should have records of flights, etc.
Sorry to hear this!
I photograph my logbook and keep the pics on two CDs, one at home and one at work. Too many priceless signatures and FAA stickers & endorsements in there!