Hmm.. Umbrella the most useful thing - go along to James Smith & Sons on New Oxford Street - they do decently built and quitessentially British umbrellas starting from about £45.
As for clothing, on the assumption you will be using an umbrella and not relying on the clothing item to stay dry, it doesn't need to be waterproof or anything as rural as a Barbour. Pea coats are quite fashionable - see here for one on sale at a decent price (although it looks a tad thin) http://www.gievesandhawkes.com/shop/online/sale/outerwear/navy-classic-pea-coat.html
I've always liked the idea of Harry's of London "Downing" shoes with vibram soles, but I get the impression the construction quality of the rest of the shoe isn't great (and at £295, not sure the price is right).
Seriously though, even in the most torrential rain, you don't really see people in London with ridiculous waterproof clothing. Just an umbrella and something reasoanbly warm.
Also, if you're coming to grad school, I assume that starts in September/October? If so, you won't get much rain - that seems to come in May, June and July.