Hi,
Don't know whether your in the British Mini Club. If not it might be worth joining. Some of the specialist insurers will give a discount for being a member.
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It might also be worth searching the forums on the BMC site for 'cheap insurance' as there are plenty of posts on there to do with newly qualified and provisional mini drivers. Might be worth having a stiff drink handy !
We're with Adrian Flux (08700 777120) on the mini scheme for one mini, and Direct line with the other, we're both in our 30's with loads of NCD but each premium is still between 190 and 280 per year. DL were about £60 more expensive than adrian flux but the policy is slightly different. Footnam James (0845 330 9771) is another specalist insurer that might be worth trying.
We have a £250 excess, a mileage limit of 10k per year and no protection on the NCD to try and keep the premiums down.
Best of luck.
Ash