I found a guidance document on the gov.uk website. To quote from it:
If an applicant contacts the IPS because they have found their passport and they wish to withdraw their application - see withdrawing replacement applications.
If an applicant contacts the IPS having found their expired or almost expired passport and they wish to continue with their passport application, the applicant must be told to return the passport to the IPS.
Where the expired (or almost expired) passport has already been reported lost or stolen and there is an LS record existing, the passport must be forwarded to the LSR Team so that they can record it as recovered. Passports returned in these circumstances will usually be destroyed by the LSR Team.
Further down in the section on withdrawing replacement applications it reads:
Where an applicant contacts the IPS to advise us that they have now found their missing passport and they want to withdraw their application it will not always be possible to comply with the applicant’s request. Please see Withdrawal of Applications for information on how to correctly withdraw applications.
An LS record must be passed if:
- The passport has been in the hands of a third party and returned to the passport holder
- The passport holder has already notified other Government departments such as FCO, UKBA or Police
- The passport was lost overseas.
Unfortunately, we cannot guarantee that a passport has not been misused during the time the passport was out of the passport holder’s possession, and our advice in these circumstances must be that the passport holder should not attempt to use the passport if it has been returned to them. Our aim is to remove as many of these passports as possible from circulation, and any such passport must be returned to the IPS for cancellation.
An LS record can be failed and any application to replace a passport withdrawn only if the passport was declared mislaid at home and the passport holder confirms in writing that they have now found the passport at home and they no longer wish to continue with the application. The applicant must also be asked to confirm that the passport has not been reported missing to any other organisation or via the IPS web site. The applicant must be advised not to attempt to use the passport until they have received written confirmation from the LSR Team that the notification has been failed.
(Emphasis in the original)
Assuming you misplaced your passport at home and it was not due to expire anytime soon, the exception in the final paragraph may apply. In that case, you may be able to re-validate your existing passport after contacting the Passport Office.
However, it also seems that in most cases your lost and found passport will be cancelled with little to no hope of ever using it again. This is probably the reason why you were told to cut off a corner so that it is clear to anyone seeing it that it is invalid.
What the IPS is most worried about is, I gather, some third party gaining access to your passport and misusing it between you losing and finding it. That seems to be the principal reason why in so many cases a lost and found passport should be sent in nonetheless so that they can destroy it. If you are certain that nobody laid hands on your passport between you losing and finding it, then I would not worry. Certainly, nobody is going to search your house and subsequently fine you for not reporting a re-found passport.
The document seems to make it very clear that previously lost passports that are sent in are not returned but rather destroyed. (I did not find any exception to that rule while scanning for this answer.) So if you want to keep your passport (e.g. as a reminder of your trips or because any visa stamp or sticker therein could benefit you in a future application to that country) do not send it in.
I cannot give you a good recommendation for how to prevent a loss in the mail should you choose to send your passport in for destruction. Registered mail so that you can trace it seems a possibility. Personally, I would probably use standard mail but you seem to have less trust in the postal system than I do.
Finally, under no circumstances ever attempt to use the lost and re-found passport for travel unless you got the positive written confirmation as quoted above. The passport will have been entered into a database of lost and stolen passports and it will flag up on the immigration officer’s monitor the second you attempt to use it to enter or exit any country that shares this data with the UK. Without having sources on hand I would assume at the very least that this includes the Five Eyes, the Schengen Area and non-Schengen EU members, probably also the Commonwealth countries – but I would not be surprised if the same database is accessible to immigration officers of upwards of 150 countries. Turning up with a passport that has been reported lost immediately makes you a passport thief in the eyes of the immigration officer – absolutely not a situation you want to be in.