Given the particular and varied nature of kit cars, you'll need to take out a specialised policy, tailored to suit the exact nature of your vehicle.
Such policies tend to cost a little more than conventional auto insurance policies but again, given the nature of kit cars, this extra expense is invariably worth it - just make sure you shop around to get the best deals you can.
Before you do anything else, you'll need to take your vehicle for an Individual Vehicle Approval (IVA) test, which acts as a kind of MOT (and generally stops you needing an actual MOT), making your car officially road legal, and costs around £200. You will need to do this if you have built a car from scratch, or reconstructed a classic vehicle.