Also London City Runner on Ludgate Broadway, EC4.
Runner's Need in Strype St, mentioned above, video you on a treadmill trying the different shoes, which I found more useful than a footscan. Their website is www.runnersneed.co.uk. Horses for courses and all that
Btw, if you were thinking of joining a running club, do that first, as most shops will give you a 10% discount. Eg Serpentine RC fees are £20 pa or £10 if you're a student. If you then get 10% off a pair of £80 shoes and a £20 running top, you're already halfway to breaking even and then you get lower entry fees to races... Alternatively, think of it as spending a total of £200 on running kit for a year (all too easy, alas) and getting club membership thrown in for free.