welcome!
I had same problem when i purchased my Z...as still had 2 months left on my other insurance - and when i phoned them - they said they cant insure me on Z (i was just under 25 then as well) and that was a company that specialises in high end cars companies like asda etc were quoting me with no problem, and they wouldnt!
Best company i found - was admiral/elephant with one of your parents as a NAMED driver(so you still the main driver) they quoted me 1600 for myself, added my mum and its gone down to 860, i was happy with that but left the payment till the morning...but they phoned me up themselves in the morning saying "lets see if i can make you a better offer" (i didnt say that i was quite happy with 860 quote lol) and they lowered it to 820. Happy days! Thats 10 month policy as well, so u get your next no claims bonus year a bit quicker
hope that helps