Hi,
I went, more than once while one of our sons used to live in London, to H&H at Bruton Street and to Purdey´s South Audley Street beautiful and iconic corner shop.
When I entered in both, the first thing I said was I was there not to buy anything, just to look around. I was treated, in both places, as if I was an oil sheik going tu buy some of their new £ 200.000 plus double rifles!
By the way, the last time at H&H, the manager, after some talk, including hunting and fly fishing in Patagonia, the guns and rods I used here, he presented my wife and me with two nice H&H adjustable cups and let my handle when I asked for, as long as I wanted, a nice used Mauser .375 H&H rifle which belonged to Stewart Granger, showing the written specifications on the book. After a while I took a book of the book store section, seated on a very confortable chair and read it for more than 15 minutes. He was very glad to let me to do all those...
This about the attention, in my case, to a non buying "alien" customer.
But, to buy a bespoke british rifle I would chose a Westley Richards one...
Good luck!
CF