How about you went to one of the following shops in London?
http://www.ukgundealer.com/southeast/london.htm
btw. they only sell to British citizen! So sorry no gun for you when you visit London.
The last time I was in London/Blackpool on business, I was in the country for less than two hours before the handgun I carried for my three-week stay was delivered to me.
It cost me around $1000 for the use, which included a holster, extra magazine and silencer [sound suppressor] A former East German Makarov, I picked it over a few of the other types available [S&W .38 revolver, L9A1 pmm Browning army pistol] due to its compactness and the nice noise muffling accessory. I might well have taken an American Colt .45 auto had one been available, but the only .45 handy at the time was an American Ingram M10 SMG, a bit bulkier than what I wanted.
Of course had I wanted to make a little noise, I could have added a couple of Dutch V40 or Brit L109 or L2A2 hand grenades for a slight additional fee, with a reasonable deposit that would be refunded if I returned them unused, or was forfeit if I found it necessary to expend them.
Unarmed in Britain? Oh no. Not for those who know their way around.