Personally I don't think driving experiance has anything to do with it... I've been driving for 4 years now, and in various cars covered over 70,000 miles and driven loads of cars (due to the job I used to do, and parents company cars etc...) and not had an accident until this year, 70,000 miles is 7yrs driving for the average person.
I have to say that I've never been quoted stupidly high insurance for the cars I've driven, but the first few years were over 700 quid which is enough.
My advice to getting the best quote is this: (i'm giving away my secrets)
1) get some quotes from any insurer, take the cheapest quote and take 10% off.
2) phone up an insurer who deals with young drivers and ask them to beat the quote you've come up with (i.e. the actual quote-10%)
3) take another 5% of that quote and phone up another insurer that you're likely to get a deal with and ask them to beat it. You should have a good quote by now, ask them to hold the quote for 7 days get them to promise to keep the quote at that price no matter what (this takes some blagging believe me)
4) in the week you've just bought your self phone a few other insurers, just to check you can't get anything better.
5)if you can't get anything else by blagging, begging, bartering, offering sexual favours (joke) etc...go back to your to the previous insurer, and get them to do another quote, just to check if its cheaper.... get them to promise again to give you the lower of the two.
Its best to do this very close to your renewlal date, because you'll be in a good position to buy there and then, and once they can smell the money they'll be very keen for your business, even more so if they think that you can get a better deal somewhere else...
Just remember you can push your luck too far, its a very fine balance between striking a deal, and getting told where to go.
I can say I've saved enough money from doing this, and will be making sure the insurance companies work very hard to give me a good quote again this year.