You need to look on your house deeds to see if it belongs to you or them. If it's yours then they cannot touch it but if it's theirs they can rip it out.

Thanks for replying. Even if the roots are in their garden, do I have any rights? Thanks

If the hedge is actually planted within their boundary, and not in yours, then its theirs to do as they want with. If you have as many roots your side, and all the topgrowth is within your boundary, then its yours - they are only allowed to cut back overhanging growth to their boundary line - the root line isn't something definitively established, since most plants spread at the roots into other people's gardens anyway.

Thanks very much. By roots, I mean the whole base of the plant above ground from which the hedge is growing. So I guess that means it's theirs to do as they want with, yes?

That would mean its their hedge, yes. Plant one of your own on your side instead.

Thanks very much for all your help. It's clear to me now that my neighbours can decide what to do with the hedge as it's growing out of their land.