Bear in mind that Peter James' policies include one that
doesn't accrue no-claim discount, as a young driver you'd be best off trying to get insurance that does build a NCD for you since this brings the cost down significantly with each year.
My Dolomite's insurance was with them and was an unlimited mileage policy that accrued no claims and still gave me a written valuation agreement just like the cherished policies do.
It didn't cost that much more either, the car would have cost me £82 on a second car, cherished policy which it's important to realise cannot be used on your only car but on an everyday, fully comp policy, unlimited mileage and as my only road-legal car at that time it did cost a whopping £85. That's per year by the way.
Before you check the above costs for decimal place disease, I'm 47, in a safe profession, have held a UK licence for 31 years (yes, from age 16) and only had one claim against my own insurance which happened in 1985.
As a first time driver/insured person then yes, you'll need to pay a bit more but it'll drop away soon enough.