So far as I can see, a parish meeting cannot be a party to a contract. This is because a parish meeting is not a corporate body, unlike a parish council. It thus has no legal existence as a distinct entity.
Where a governmental corporate body ceases to exist, there is normally a successor authority.
In the case of a parish council that ceased to exist as a result of the 1972 reorganisation, I would imagine that the district council would be the successor body, and would therefore have become party to the lease. It seems as if your best course is to discuss the matter with the district council.