What a nasty job, esp those raspberry canes. Unfortunately plants do not respect boundaries & you'll be fighting their will to live. Discuss with offending neighbor to thin out his lot.

The only remedy i can think of is a membrane between the two gardens, but it sounds as though your hedge goes right up to the boundary which makes it impossible. Would your neighbour be understanding enough to allow you to put one on his side?

Ordinary weed membrane won't do the job - it'd have to be a strong root rhizome barrier such as that sold for bamboo, and it would have to be inserted vertically. Lilac trees are renowned for producing suckers far and wide, and raspberries, unfortunately, are also known to 'walk' some feet away. From personal experience, its just a case of digging out the intruders on a yearly basis, unless you're able to insert a barrier to prevent recurrence, but it doesn't sound as if either of those solutions is an option. If you have available something like SBK brushwood killer (its a liquid, like water, and kills tree stumps), you could cut down the lilac suckers, drill into them at soil level, or make cuts (better if you can drill), then carefully apply SBK to the wounded areas without spilling it anywhere else (including the soil and any plants nearby), cover with upturned flowerpots and that will kill the suckers. SBK is available on Amazon in the UK - you may have something similar where you are.

Bamboo, would treating suckers with SBK damage the parent shrub? I have blackthorn sucker trouble big time but don't want to kill the parents.
(Apologies Gator for muscling in on your question...)

Me too Stera! Old apple trees and the lilac are doing this, so would like to know the answer.

Yes, its possible that it might damage the original plant, but its not likely - in order to kill something with a thickish trunk, it'd need a lot more wounding and SBK to make a dent at all - even applying SBK directly to a tree doesn't kill it unless you cut it down to a stump first, though it might make it look a bit sick for a while. It might have more of an impact on something like raspberry canes though...

Discuss with your neighbor first or you may be held liable for damages. He may even do the task for you. Good relations go a long way.

Thanks for all the helpful advice!! And "horn in" all you want - love the feedback. That's how we learn. I want something fast and effective without a lot of work. Planning to experiment a bit. Thanks everyone!! :)

Fast and effective - well you might have to find a genii for three wishes there...

You could always leave them and enjoy the free gifts of flowers and fruits!