We back onto a house which has Leylandii planted and which have grown very high and overhang into our garden. I can’t cut them back to the party wall as the foliage is brown so am wondering what can I do to prevent them continuing to grow and overhang the shared wall as we are losing significant amount of space in our already small garden. Would erecting a trellis stop them from breaking through?
They will outgrow any trellis and grow through it in any case.
Your best bet it to try to make an agreement with your neighbour to keep the hedge to a reasonable size and perhaps sharing the cost or effort of annual clipping at the desired height.
There is no other way you can stop them growing as they are not your trees. Unpruned, they grow very large and cost a lot to eventually remove, and you neighbour might not realise this now.