Greenwich (NMM) and the Science museums now have very little in the way of model ship displays. The management didn't think it appealed to the 'yoof' of today!! The Greenwich collection is in climate controlled storage in Chatham, Kent. You can make an arrangement in writing to visit and see some of them but will need to specify which vessels. Not very useful. The equally impressive collection at the Science Museum is also in storage and not available to the public. When I was a child I used to roam London on my holidays, the model ships were a delight, I visited the museums 2 or 3 times a week.
I'm afraid Portsmouth hasn't much to offer in the way of models, even though it has the largest collection in the UK there are not that many, most are modern warships. But there is Victory, Warrior and the Mary Rose. All in all, I think Portsmouth is your best option, you'll need a full day, and if you're luck, I'll buy you a pint!!