I'm currently insured 3rd party fire and theft. When I take out a new insurance policy with a different insurer I will want to go fully comp. Does a NCB from a 3rd party insurance policy count OK for the fully comp policy, or might the insurer say that only NCBs from a fully comp policy are taken into account on a fully comp policy?

NCB is NCB, it doesn't matter if it's from a TPFT or fully comp policy.