The problem is, its a pretty useless piece of legislation (and was brought in as a bit of a knee jerk). It totally fails to deal with the problem of hedges which get wider as they grow (ie which gives you the unwanted problems arising from having to trim it on your side when the hedge owner fails to do so.) High is one thing, but wide is another.
Second problem is that even though it is a legal responsibility, your local council is probably unlikely to want to act - partly through lack of resources, but partly through lack of inclination. And very likely through lack of any internal process for dealing with the issue. (If the responsibility has not been formally "delegated" to a particular person or service, then there will be no individual formally/legally authorised to deal with the legislation on your behalf. And chances are it hasn't) Sad fact, but unless you are very lucky, it will probably take a lot of effort on your part to get the council to do anything.
Unfortunately, long experience suggests the most practical solution is to trim it youself - not satisfactory, but practical. Do it regularly - a little & often causes you less issue in getting rid of stuff than does cutting off masses in one go.
And yes, you are correct in that you should not dispose of the cuttings without first asking him if he wants them. Ask in such a way that you only have to ask once - rather than every time you want to do it. Do not just chuck it back over his side - that just leads to further conflict (and, in fact, if you happened, break or damage something of his by doing so, he could sue you for the damage!!)
Good luck ...