Paul King wrote:

I used some excess DPM instead of proper tile felt under the tiles of the
roof of my shed when I built it (well - its only a brick-built shed...)

The damn (no that should be *&$£"!) squirrels which live around here have
managed to get into the roof space and have gnawed several holes in this
DPM, with the result that the shed is no longer "dust proof" from the crud
which blows in under the tiles.

So, what would be the correct kind of glue to use to glue DPM patches over
the holes?

I reckon its a polythene DPM - its a blue "plastic" - but I've never come
across a polythene glue...

You could try silicone.

Polythene is an olefin, and they are buggers to glue.
Contact adhesive may work - solvent/rubber stuff like teh old evostik.