I rang a few up to ask and all said they accepted the no claims history. Some had an option box to say it was gained via the scheme.
I got quotes from online comparison sites and a few others not on those sites and ended up going with the company we have house insurance which was cheaper, when they included a discount for having a 2nd policy with them and gave the cover I wanted and needed. Mostly i do it online though as is easier for me.
I guess it depends on many factors as to how much your premium will be, but always worth shopping around. I did end up having to do it over the phone with them as for some reason my private plate was not being found on the database online and would not let me proceed.