I've no guarantee that this will work but it's worth a try. Download and print this form:
http://www.direct.gov...alasset/dg_175799.pdf
Complete it to the best of your ability, including entering your own details at Section 5. Then send it to the address at the bottom of the form, enclosing an explanatory letter
OR
Download the form. Fill in as many details as you can, on your daughter's behalf. Then simply get her to sign it before posting it. (If an explanatory letter might be needed, to explain why there's no police reference number, type one out on your daughter's behalf and, again, simply get her to sign it).
Chris
PS: I actually sympathise with your daughter's viewpoint. If my passport got nicked (and I had no further use for it) I'd probably not bother reporting it and simply wish 'good luck' to anyone who could find some nefarious use for it ;-)