turan:not helpful
With respect, I think Skywalker's comment was probably the best advice you will get!
You are 17, held your licence for 4 months, no one else in the family owning a vehicle, live in the centre of London and a student! I have no idea why you are complaining about the premium?
You will find it cheaper than £3,500 and you will find that TPO cover is almost redundant so you should opt for TPFT as the cheapest option, or Fully Comp if the value is over £5000.