Yes, I thought so. That's what we found when following an earthquake our premiums rocketted. They admitted they didn't want to insure us, and that they were declining all new business but they had to offer us a renewal.
Price made your eyes water though
Of course, if as the OP suggests the previous owners had been economical with the facts then all bets are off
Friend has a house that was hard to insure for various reasons. He found a mainland european insurer that was more than happy to take it on. Had to go via a specialist broker but it was very reasonable pricing IIRC. Was a few years back mind...
Darren