First stop, Victoria & Albert Museum. There are some splendid examples of art metalwork in the Metalwork Gallery, including a Wilkes 'cavalier lock'. Also somewhere in the V&A is the 'Beddington Lock': a fine example of high relief craftsmanship in wrought iron, still with traces of its gilding.
Nearby, the Science Museum has dismantled the Locks & Fastenings Gallery, but some of the items were put into the Household Gallery. The reconstruction of Bramah's shop window, with the Challenge Padlock, was on show there. Years since I've been in London so not sure what is on show, or where.
In the City, the Museum of London has some roman and other locks. But perhaps you have already seen some of those
Also in the City, you might like to see the Bank of England Museum, just to say you've been in there. And the Tower of London, have a look at the Crown Jewels — and their accommodation.
Hampton Court Palace, up river, is worth a visit for its magnificence, following some restoration work.
The Wallace Collection is noted for its armour, and paintings, but if I remember correctly, some other metalwork includes a few locks and keys. It's in Westminster so not far to go, and not that big, so you could make a quick visit.
Bramah has no museum, but if you contact Mr '
Jeremy.Bramah@bramah.co.uk ', and can promote Bramah locks in Italy, he might see you.