Under the Law of Adverse Possession, a person may apply to have land that he/she has occupied for at least 12 years continuously, registered as his own. This is more commonly known in the popular press as Squatters Rights. Since your vendor has been in possession of this land for greater than the required period, this is what he would be able to do. The vendor could alternatively supply a purchaser with a Statutory Declaration to the effect that he had been occupying it for greater than 12 years, such that you could register claim to the title with the Land Registry. Then the land on which the extension sits becomes legally yours. The idea of indemnity insurance is a further belt-and-braces measure to ensure that if a challenge to the claim emerges from the woodwork, you would be compensated.
This is presumably what your solicitor is telling you and it always intrigues me about these questions that folks appear to mistrust their professional advisor to the extent that they want a second opinion from an anonymous (but hopefully accurate) website. I trust my view aligns to that of your solicitor.
You may wish to renegotiate your offer on the basis of the aggro of having to go through this process. Your solicitor may anticipate slightly higher fees - there's more work for him - ask him. But you will end up owning the land.