UK passport - frustrating situation

Excellent, thanks both.

The guidance on renewing a passport might be helpful:
https://www.gov.uk/renew-adult-passport/renew

Specifically the section on unexpired visas - it suggests you "send your previous passport with the visa attached to it with your application. Your previous passport will be returned to you. You'll be able to use the visa if you carry both passports."

You might want to order a special 50-page passport while you're at it. My hunch is that the cost of renewing a passport will be no more than applying for a second one. From what I've read owning two passports is really only open to government employees or businesspeople who get it done through their place of work.

There's also an emergency travel document:
https://www.gov.uk/emergency-travel-document

One of the criteria is that "your passport has been lost, stolen, damaged, is full, has recently expired or is with HM Passport Office or a foreign embassy", but it seems you can only apply if you're outside the UK, it costs £100, and it sounds scary.