Paul D.Smith muttered:

Firstly, I've read that you want to stop it ASAP because the longer it is
there, the more established it becomes. Secondly, at Kew Gardens we saw a
similar section of hedge and they were doing the following.

Implant tall cane wigwams (taller that the surrounding hedge) - bindweed
loves to climb as high as possible
Wait for a good covering then spray the wigwams with systemic weedkiller
Repeat until it's all gone

So I should do this in spring...

In my organic garden, we've managed to get it under control by ruthlessly
digging up where we can dig and breaking it off at ground level where we
can't. If you break if off, the stems shrivel up and die and it drops off
by itself. I would also remove flowers in case they manage to set seed,
although they do this far less readily that, say, dandelions.

I've been doing more or less this so far - next year will be a different
matter tho!

Eternal vigilance is required to attack as soon as it is big enough to spot.
If one does slip under the radar, it puts up a white flower to taunt you and
then the wrath of the gardener descends upon it ;-).

Many thanks.

Good luck,
Paul DS.