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Based on owning many rubbish cars over the years I'd say £1500 is just too little for a reliable car. Better to just use car shares when you need them. A £1500 car is almost definitely going to be problematic in terms of ULEZ or will fail an MOT and end up getting written off sooner or later. £1500+insurance and tax and repairs is a lot of car shares. I'm sure there are exceptions to this but you'd have to be really lucky.
Are you in London?