Originally Posted by
leaveamessage
Make an appointment for a same day renewal. Do not tell them it is damaged.
Turn up and plead your case at the counter.
Officially you are not supposed to be able to get a damaged or lost via the same day service. Unofficially, they can and will do it at their sole discretion - I know this from personal experience a couple of years ago. Nothing to lose by trying

+1 I used to contract for the IPS (as they were known then) and can confirm this is the only way you have any chance. Make sure you get a timed appointment.
Do not report it lost or stolen - this is not only illegal, it will delay your application, since the passport will need to go on a special register. You will also need to fill out a legal declaration (form LS01 if I am not mistaken) that it is lost/stolen as well as reporting it to the police if stolen and getting a crime reference number. You will also go though a more thorough security check, more like a first time application rather than a renewal.