Depends what you are going to do. If you want to start running (as your name suggests) then I would advise getting fitted for a pair of trainers. Sweatshop is good and have quite a few outlets, they will check how you walk / run and recommend a trainer to suit. Store Locations
Else there must be a 'proper' running shop somewhere near you.
Your £15 trainers may well be ok, but ime a proper fitting trainer does help and does help to avoid injury.