How much of your budget is for the insurance?
Given your age and where you live any BMW with serious performance will be mighty expensive to insure.
Therefore, look at a diesel, or you might find an i3 for £15k, no ved and no London emissions charges.
They are quick - 170bhp but max torque from 0mph and no turbo lag or gearchanges but you need to be able to charge at home on the off peak, which costs pence.
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