Try the millions of Sports Direct that are littered all over the place, that's where I get mine from.
Is that the place in Brentwood? I'm sure there must be somewhere, perhaps more on the outskirts rather than in central London. Though if you go out to the edge of London you might as well get on a train and go to Brentwood, it's only 30mins or so from Liverpool Street. All the general stuff can be found in a good Sports Direct (boots, wraps etc), though they don't do gum shields and head guards.
Sports direct is the las place u want be going for boxing gear it's all crap. The only place is sugar rays what I know of
The low cut boots you can get in some Sports Directs are identical to ones you can get in Sugar Rays. Wraps are too. Like I said, if you want anything else you'd need to go elsewhere.
Sports Direct only does Lonsdale and the low-end Adidas and Reebok boots. Not great. Think Sugar Ray's it is...