Best time is once any birds which might be nesting in the hedge, have gone. However if needs must you can do it any time. The nice thing about all those trees is that you may cut back as hard as you need to. They are chosen for hedge precisely because they can stand any amount of hard pruning.

Gosh that hedge is sort of taking over the pavement isn't it! Agree with Owdb. wait until any birds have fledged if possible but if your council is having words with you...

Good luck with the hedge, mines is getting a severe short back and sides soon too x

I cut my yew edge last Saturday (but it was more of a trim than a hacking back)

I must say as a first visit to GOY I am impressed with the rapid responses.
Thank You
On reflection the question should have been more specific,how far can I cut back and still ensure a modest re-growth this season and maintain the aesthetics and privacy.

As your hedge is not leylandii you can cut back as hard as you like and it will regrow. Cut back to the depth and height that you want and there will be a little regrowth this year and more next. At least that is how I would do it - Andrew is more knowledgable than I on hedges.