Yep if you can get proof of your no claims bonus (or claim free driving period), that is enough to get them to give you the discount.
I spent my first 2 years as a named driver with Churchill. I then had the policy cancelled, and started my own policy with Sky Insurance, who offered me a 2 year no claims bonus, for having 2 years of claim free driving

All I had to do was send copies of 3 insurance certificates from Churchill (start of policy, end of first year, end of 2nd year).
All insurers would be different I imagine, but that should be enough. They offer no claims discount, you have proof of your no claims, they should honour the discount
