As a first time main driver, I got mine for £725 at the age of 20. I was getting similar quotes at 17 but I think that premiums have gone down slightly for young drivers since then (don't know why).
I'm with Diamond ("car insurance shaped for girls" but they can't be selective since the EU ruling, and you get £300 bag contents insurance for free), which is a subsidiary of Admiral. Most of my friends who have cars have insurance policies with Admiral and it tends to be cheapest for young people.
Admiral owns Confused.com, so you'll generally get the cheapest quotes by using that particular comparison site (approx. £50 cheaper than GoCompare, which I was using before I realised).
It's nearly always cheaper for young people to be fully comp'd. I added business use to mine (to cover commuting to multiple places of work) and that brought the premium down by a small amount as well.
Experiment with job descriptions. Martin Lewis published a 'Car Insurance Job Picker' where you can see the difference that they make, although it was last updated in 2009 so caveat emptor.
Then add some named drivers. Adding my parents reduced my premium by £150 each(!)
Don't over-estimate the annual mileage because that has a significant effect.
Experiment with the other options, like where the car will be parked overnight. Bizarrely, parking my car on the drive actually INCREASED my premium, whereas parking on the road reduced it.
If there's a choice of insuring the car at another address, get a quote. eg. I live in Sheffield when I'm at university, and the premium from there is approx. £200 cheaper than from my home address with an Oldham postcode. I spend more than half my time in Sheffield, so I think it's fair to do that, but you should be careful that you're providing accurate information.
I think that the comparison sites blacklist you after you do too many searches (this happened to me after about 25 in one night), but you can still get to the results of previous searches, then click through and fine-tune the policy you want on the insurer's own website.
Hope this helps, PM me if you have any specific questions.