I am in the same boat so contacted my current home insurer Aviva, I told them i did not have final sign off from BC.
They were happy to provide cover on the proviso that they would not pay a claim that was a result of poor workmanship, quite what difference to that final sign off would make Im not sure, as BC don't see everything.
Premium was the same or cheaper as i went from a 4 bed to a 3 bed, the.y have actually covered both properties for 30 days as my site cover expired before the completion date for the sale of my old property.