you may have to use environmental control or chemical control, you could shade or cover the ivy in a thick blanket or whatever to block the sunlight from it meaning it would start dying but this can take a long time for it to decay, chemical control is easier but you risk killing and wildlife living in it or around it. the only way to truly deal with this is physical control and that is pulling it out but this can disturb the rockery and possibly destroy it, but for me the pulling it out is easier and safer so it looks like you will have to rebuild it again.
happy to help :)

I've seen a photo of it, Hank, I remember it well ,what a nightmare I thought, don't fancy trying to get rid of that lot...

I reckon, if you've the energy and time, it would be best to rip the structure down, dig out what ivy roots you can, treat any roots you can't dig out with SBK brushwood killer, and then, when you're sure you've got all the roots, rebuild. The trouble is, the roots might well be under the paving surrounding that raised part too...

O.M.G. Right, thanks for that guys, I must say I expected it. Actually I fantacised about pouring petrol on it and settng it on fire - but since this hasn't been mentioned I guess I can forget it.
So I'll forget it for now and carry on with the hedge whilst giving it further thought.

Setting fire to it would definitely damage any wild life in it. Probably not a good idea and in any case it would not kill off the roots.
You do not need to throw away the stone, that is re-usable. And I find that ivy toots do not re-grow as readily as say Couch or Bindweed. If you get the majority of a root out then it does not seem to throw up new growth. Having said that, it is no easy task, I have done it!

If it is so bad that you don't want to show a picture, Hank, then I think that the easiest thing to do would be to dismantle the whole thing, clean up the ground and rebuild. Keep you warm and busy during the colder days and it will be all ready for planting up in spring!

Nothing to add to all that except heartfelt encouragement!

I think you'd be wrong to dismantle the rockery - it will be nicely weathered under the ivy and you'll lose that naturalness, no matter how carefully you rebuild. Clear the ivy away before making any quick decisions.

Thanks again all, i'm still working on the hedge, and by the time I've finished that I'll have made a decision about the rockery.

Its all go Hank!

Half the hedge already gone and the rest should be by week end. Am enjoying the work.

Good, nothing like a project is there. Worth the aches and pains afterwards, lots of hot baths!