I spent 2hrs looking the other day, and as far as I can tell, it can't be done.
Tempcover.com - max insurance grp 18
Norwich Union - high insurance group must be 25 years +
eCarInsure - min age 25 for anything
Dayinsure - min age 23, min age for high ins gp is 25
Budget - max ins grp 18
Insuredaily - refused to quote combination of age/car.
Your only option is to get someone aged 25+ to drive it for you, it would seem. You could also take out a full policy, and cancel it during the cooling off period, which means you'd get a full refund -£20 admin charge. Though I'm not sure what the implications are if you setup a policy with prior intention to cancel - check that it's legit. I decided not to myself, as should you need to make a claim, they'll keep the whole policy - plus whilst you do get the refund, it would probably tie up your money for a good few weeks/months.
If you have another policy - you could be able to add the car to your policy temporarily, depending on who you are with.
If you can a way to do this, do let me know, as I'd love to know for future reference.
Ben