Emrys Davies wrote
You say "I don't care about the hawthorn either. The whole lot must
go!!"

So that makes the solving of the problem fairly simple. Dig up the
hawthorn and then dig up the bindweed roots making sure that every
morsel is removed.

Ha! The roots are notoriously brittle, and fragments only nanometers
long will re-generate.
Any that escapes your attention will soon reveal
itself via new weakened growth which also needs careful removal. By the
end of the summer you will be bindweed free.

I would have a thorough check for birds' nests, and wriggle under the
hedge to locate and snap the bindweed at base, dripping a bit of strong
Glyphosate on the broken stems. This will check the bindweed for the
time being, if there are birds nesting.
--
Roger Hunt