The purpose of indemnity insurance is to cover any enforcement action the council might take for lack of building regulations approval/sign off. It would cover your legal fees in the event that action was taken, the cost of any remedial works required, loss in the value of the house due to the issue, cost of surveyors etc.
As you have contacted the council, the indemnity insurance provider won't now cover the issue, as the risk of enforcement action is much greater. From a mortgage lender's point of view, in the absence of an indemnity insurance policy, they will require evidence of building regs compliance. So the seller's only other option now is to obtain a regularisation certificate. This is assuming the work would have required building regs in the first place. If it didn't, the council can inspect and confirm this, and then everyone can move on
If it did require building regs, but doesn't have it, it can take days or weeks or months to sort out, depending on the council's turnaround time and whether the work does actually comply with building regs already or not. It usually involves exposing part or all of the beam, which may mean cutting away part of the wall, which will then need to be re-plastered and redecorated presumably. It's not a 5 minute job. It will take even longer if the work doesn't comply and needs to be rectified.
I imagine your solicitor is frustrated with you because you are paying him/her to sort the issue and advise you of the legal consequences of things, but
you have gone ahead and taken matters into your own hands, presumably without any real knowledge of how the system works. I'm sorry if that sounds harsh, I don't mean it to, but I can't think of how else to put it. You'd be surprised how many people do it
He's also now got to tell the seller's solicitors which won't have been a pleasant conversation.
The seller might be annoyed because it's not really your place to report issues with their property to the council and potentially cost them a lot of money. I can't see how they'd be able to sue you though. If the work should have had building regs and doesn't, the seller should have got it done properly in the first place.
From your point of view, having a regularisation certificate is much more preferable to an indemnity insurance policy. As long as you're happy to wait as long as it takes for the council to inspect the works and for any remedial works to be carried out, and the seller is willing to sort with the council, then hopefully all should be fine.
Just remember neither party is legally tied into the transaction until contracts are exchanged.