What should I do if I've lost my passport with a DTV visa issued in London?

Isn't this more of an issue if your visa is a traditional sticker? Can't see the problem if it's an e-visa. Perhaps you could travel with a printout of the information page of the old passport but like someone else said, if it's possible to get an annotation in your new passport at a local immigration office, that's even better.

This will become a recurring theme with a 5 year visa. Many people will need to get a new passport during that time.

It’s not an issue. If your old passport linked to the DTV has expired just carry both passports with you when you travel.

If you’ve lost the original passport then you need to go through the steps of getting the entry stamp and notation on the old passport in the new one - which you would do at a local immigration office. Once done you shouldn’t have any issues travelling with the new passport and recorded stamps detailing the link to your old one.

My friend lost his British passport in Phuket, once he organized a new one he went to immigration and they transferred the DTV for 1000b

This will be a good one to follow ,

I believe some one else enquired about it and was told they had to re do there visa since it’s MOFA visa not issued in Thailand. ( I don’t know how true this is) and I hope it’s not accurate.

But I was you I would reach out to london embassy and explain your situation.

Other people may disagree with my next statement, but you could also try enter Thailand on your new passport with a photo copy of your old passport and your visa , best case they stamp your DTV, second best case they give you a 60 day exemption. Worst case they send you back to where you came from.