It really depends what you want in terms of accommodation, and whether you're prepared to live somewhere a bit "edgy". You can still find "reasonably priced" accommodation not far out of the centre.

My son, for instance, has lived at various times in the last 7-8 years in Bethnal Green, Hackney and Dalston. At present he's in a flat-share in an "ungentrified" part of Dalston, where he pays £95 a week for a room and shared kitchen/ sitting room in a reasonable flat...."reasonable" meaning in good decorative order and not a "studenty grot-hole". The flat's decent, but it's on a street above a market, and noisy during the day. But as he and his flat-mate are out working while the market's operating it doesn't bother them, other than Saturdays.

I'm quite happy to visit where he is now, and was happy to visit his previous place, about 3/4 mile away. I *wasn't* happy to visit his place when he lived in Bethnal Green. I always felt nervous on the street there. The ethnic and social mix wasn't much different from where he is now but the street itself "felt" much more intimidating....and he is noticably more relaxed where he is now when out and about.