You 'can' cut it back to the trunk but it will not regrow at all, possibly this is what you want :-)

The 'green' on a leylandii is only a thin surface coating; behind it the needles will be brown and will not grow back. If you cut it halfway back to the trunk you will be left with a dead looking hedge. If you cut it all the way back to the trunk you will be left with a dead looking hedge with 'sticks' along it. This should not affect your neighbours side which should still be thick and green.

Many thanks. I knew that it wouldn't grow back, but I wanted to use the surface to grow climbers on and to have space to grow other shrubs. It was a choice of doing that or putting up a wooden fence, which wouldn't allow nesting etc. Also I was concerned about my neighbour and so, thanks to your comments, it wouldn't affect them at all. Many, many thanks !!!!

Sorry Wellend even if you cut the hedge back to the trunks you will still not have an area to grow climbers and shrubs in. All the nutrients from the soil will have gone to feed the hedge and the roots from he hedge will mean that the soil is totally impoverished. You will have your work cut out to get the soil into anything like condition to grow anything else... Good luck!