They are being stupid. Just plain stupid. Sure, they can't do a new one, any more than in the states they would issue a new W2. But they have photocopies and computer backups of everything, so they sure as shooting can give you a COPY of what they did, either a photocopy or simply typing all the information from the P60 into a Word doc or email.
If they refuse, tell them you will report them to the HMRC for obstructing your legal obligation to file and pay the correct amount of tax. Remind them that under the DATA PROTECTION ACT, you are ENTITLED to EVERYTHING they have on you. EVERYTHING. They can NOT refuse you your information.
Alas, also under the data protection act, they have the right to charge you for this information, but no more than a "reasonable" fee. Hopefully, they won't do this.