How to find my landlord?

G_M

As tbs and others have said this is clearly an amateur and unprofessional LL. You now have a choice:

Go along with him by accepting lower rent, arranging yoru own gas certificate/repairs etc at his expense and trusting that any repair etc problems in the future will be dealt with or

Make a nuisence and insist he arranges the certificate, insist on knowing about mortgage lender's permission to let and HMRC etc.

Since there is ongoing doubt about where he really lives, there is still a possibility of the tax becoming a future issue (I'd certainly want a written confirmation that he is not a non-resident LL for tax purposes).

I'd also want to be sure the deposit is safe - with an approved scheme.

How much you rock the boat beyond that is a matter of choice.