Question

can a Parish Council make donations to a non constituted pressure group

Answer 1

It's very difficult to answer that without more details.  First of all, the answer depends on what the pressure group is trying to achieve.  The aim could fall within one of the statutes that give councils the power to act, in which case the wording of the particular act would be relevant.

The other aspect is exactly what is meant by "non-constituted".  There is no requirement that I know of for a recipient of a grant from a local council to be an incorporated body, such as a limited company.  But it would certainly be desirable that a group have some formal existence, such as simple rules about objectives and membership.

So the answer is probably yes, but subject to caveats.  And if Section 137 is used to justify the expenditure, then it always has to be based on a commensurate benefit to some or all of the people of the parish.