John
I am a bit of a cracked record about this on GCA, but it always takes a lot longer to get around the UK (by road), and especially in the crowded south-east/London area, than visitors expect. Both Hunstanton and Brancaster can be (at least) four hours' drive from central London and Worlington perhaps two and a half, of which getting out of London will be (potentially) at least an hour, depending on when you choose to travel. Of course if you head out late in the evening these times will be reduced. Nonetheless this is by way of saying that an East Anglian trip should ideally stand on its own, and not really as an annexe to a London-based outing.
London to Worlington to Hunstanton to Brancaster, with Sheringham (coastal) or King's Lynn (wooded) or Thetford (heath/woodland) or Flempton (fun heathy nine holes not that far from Worlington) as an additional stop if another venue is required, is a classic golfers' route.
London to Ipswich (Purdis Heath) to Woodbridge to Aldeburgh and Thorpeness is another excellent East Anglian itinerary, more predominantly heathland but close to the sea, this time a bit further south in Suffolk (and thus a bit closer to the capital).
One thing to emphasise is that several of these clubs (and especially Worlington, Brancaster and Aldeburgh) are basically two-ball clubs, with a strong tradition of foursomes golf, and so you do need to plan any visits accordingly.
Overall though it's a terrific part of the UK for golf, much more visited ( I suspect) by English club golfers than you might discern from other sources, with lots of fun pubs and places to stay (to that extent rather like the Bournemouth area, a classic location for English-golf-club-based trips). And I have to disagree a teeny bit with my friend Sean with my own East Anglian ranking, which remains Brancaster (1), Worlington (2) Hunstanton and Aldeburgh (=3), and Woodbridge a very close fifth behind - with 'fun' and 'quality' in this case synonymous.
Hope this helps!