How the hell did you get it so cheap? I just looked to get a quote, £189 a night!
You're right, rates are through the roof for that weekend. Just had a quick scan for you, based on 2 nights when Muse are playing. Three good hotels around your budget jump out at me, Club Quarters St Pauls, Hilton Canary Wharf, De Vere Devonport House.
The latter is Greenwich/Cutty Sark which is a bit out to be honest though...but it's a nice hotel mind. Hilton Canary Wharf is a bit out but it's a two min walk to the tube, and it's direct to Wembley Park 35-40 mins on Jubilee Line.
Club Quarters St Pauls is probably your best bet. I've stayed at all three mentioned and can vouch for them.
Booking.com is showing them at £230-250 for two nights.