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There are two ways:
-Just paint it now, maybe take off all visibly loose stuff with a scraper first, paint with primer (peel stop as primer sounds great, but I am not in the UK so don't know the product) key with fine grit, paint. Have a way nicer door.
-Get rid of ALL the paint, different ways to do that. Then filler, sand, prime, paint, sand, paint, maybe paint a third time.
Have a perfect door.Always first option here (if I am not just touching up) as we are renting, and I am not investing several days of my life making other people's stuff perfect for free.
A photograph would help to get an idea but it sounds like it should be sanded/filled/primed/undercoated and 2 top coats which is a lot of work but all pretty normal for decorators.