Typical new driver policies usually start from around �2000, so you're probably not going to find figures much lower than the ones you're currently being quoted. New drivers are far more likely to cause an accident. If that accident results in another driver needing lifetime medical care, the insurance company might have to pay out several million pounds.
I've seen posts on some websites suggesting that you should try asking for quotes for '3rd party, fire & theft', or even for 'fully comp' as, somewhat strangely, these sometimes come back with lower figures than simple 'third party only' quotes. (I've no idea whether it actually works for young drivers but it might be worth a try. I do know that my own insurance is cheaper for 3rd party fire and theft than for 3rd party only; so there must be some truth in the idea).
Martin Lewis is the acknowledged guru of money saving. (He appears regularly on several TV and radio programmes and is frequently quoted in the press). His website recommends using this wizard to find out which specific insurers you should check out:
http://www.moneysavingexpert.com/redir/532214e c
It also suggests checking this out:
http://www.swinton.co.uk/car/youngdrivers/
However, his key advice is to combine several different comparison sites, and to also to check those firms which don't appear on such sites. See here:
http://www.moneysavingexpert.com/insurance/com pare-cheap-car-insurance
Chris