If there is no planning for the extension, the sellers can put in a retention application which will take a few months and cost them. It depends on how big the extension is. If it’s small, they may decline to go retention. They may chance getting your solicitor to put in a qualification on title to your bank saying there is an issue with planning. It’s up to your bank to decide if they will lend.
However even if they approve, the phase “the day you buy is the day you sell” applies. It’s our problem then. You’ll have same problem when selling or remortgaging in future. Just because a bank is okay with it now doesn’t mean they will in future. I’d be insisting they fix it but you do the get the whole attitude with some sellers that they will chance selling to someone else who won’t insist on it to save them the time and money so take it or leave it. Listen to whatever advice your solicitor says on this.