I wouldn't have thought you would have any problem as long as you're not maxxed to the hilt with points on your license
Insurance on kit cars seems very favourable for the younger generation when compared to the run of the mill Novas, Saxos etc.
Ring up a few insurance companies that are listed on this site under the 'Support services' section and find out - bit of leg work required but it's the best way.
Cheers, John
Madabout-kitcars.com