There were good running shops in Croydon (Surrey St Market), and in Kingston (across the bridge from the town centre), hopefully they're still about. Both of them had treadmills for gait analysis.
Sweatshop also have a few outlets in London. My only experience of their shops, at the Covent Gdn branch, wasn't great, but I do buy from them online.
I've heard that ASICS have a flagship shop in central London which is good, but of course only stock the one brand.
Nike have a similar shop (Niketown?), but they do a lot of other sports, and also make a lot of their money from fashion purposes, so I'm not sure if their service is as good to runners, but have no first hand knowledge. (Had good service many many moons ago from the old Nike Pegasus, but then they seemed to make their shoes narrower, and I switched to New Balance. 20 odd years later, and a couple of pairs of Mizunos not withstanding, am still with NB.)
London Marathon used to have an outlet in Covent Garden, would expect them to be good, but don't know much about them.
I'd go with that advice. Run & Become, just opposite New Scotland Yard have the personal touch and time to sort you out. It's a bit frustrating on occassions to shop there, as the till is manned only if one of the assistants happens to notice. They're a first class service by any standards.
As for Sports Direct, trying to move in the place is a challenge as the isles are 'chokka' with kit. They have some serious sports kit bargains if you manage to weave your way through the tourist and chav element factor, but as before, if you know what you are looking for, worth a punt. Worth getting there around 10am while the street is still quiet.
TTB and I use this place to pick up cheap 'Croc' shoes