You’ve no right to purchase the freehold initially (enfranchisement) but the outgoing seller may have; it could be something that they take on prior to exchange if they’re desperate to sell.
Alternatively, you can make an application for the crown to disclaim their interest in the freehold. I haven’t done one in quite a while but last I did, Farrah & Co were the solicitors that acted on behalf of the crown. Be prepared to pay a sum for the freehold AND their costs. I’d consider reducing my offer in line with the same.
As your solicitor says, there is no drama and the risk is insurable but a lay person buying a home is not often in a position to assess the risk so your eventual buyer will be just as worried as you are now.