No, you can not.

Once a passport is reported lost it is invalidated and placed in a database called the Stolen and Lost Travel Document database managed by Interpol. Attempting to use it in the UK or any other country that uses the Interpol SLTD database (which includes most countries globally) will at a minimum result in you being denied travel and potentially detained at least temporarily whilst the details of the document are determined.

This is what the Home Office guidance says in its document Guidance for paper passport applications (p6):

Section 3: Details of previous and current passports held

Uncancelled passports

Lost or stolen

If your passport has been lost or stolen, but you haven’t reported it yet, fill in part C. Give us as many details as you can and tell us how the passport was lost or stolen. Please use section 8 if there is not enough space in the boxes provided. If your passport was stolen, report the theft to the local police and include the crime reference number at section 8. We will cancel your lost or stolen passport when we receive your application.

[emphasis added]

So at some point when you applied for your new passport, you already gave them details of this one & it has been cancelled. They then go on to say:

If you later find the passport which you reported lost or stolen, you must return it to us. You will no longer be able to use the passport. You may be held by the immigration authorities or the police if you try to do so.

As others have said, all passports reported as lost/stolen are cancelled, and cannot be used.

The UK Passport Office used to require any subsequently found passports to be send to them. The main advantage of doing this for you, is that they record how often you lose your passport. If you make too many reports, it can be more onerous to get a replacement passport in the future. Returning the found passport may remove one of these counts against you.

I can't see any current requirement to return your found passports to them (they do provide details of what to do if you find someone else's passport). If I were you, I'd probably return the passport with a covering letter to them. One address is

HMPO, Globe House, 89 Eccleston Square, London, SW1V 1PN

No, you can’t if you already have a new passport, because then that passport wouldn't be registered any more, so you probably have to file for a replacement.