Does pruning a leylandi cause it to grow higher?

No, that is rubbish. A plant will grow a certain amount each year and leylandii's are no exception. If it is overhanging your property you have every right to trim it back to the boundary line.
Are the leylandii's forming a hedge? Are they over 2 metres tall? You can ask your neighbour to have his own trees trimmed otherwise he will be in breach of section 8 of The Anti-social Behaviour Act 2003 and if he refuses to trim them and keep them trimmed, you can get your local authority involved, it is all set out in the above statute. If you need to ask me anymore questions, I would be happy to help, leylandii's are the scurge of the planet and should all be burned!!!! They are dense thugs which suck all the goodness out of the soil and nothing will grow within 6 feet of them and they have even caused a law to be passed about them because they have caused so many disputes over the years between neighbours.
I gave another member similar advice a few weeks ago. The information will be in my Outbox if you want to have a look

ive never heard of that but if you cut the tops off they will bush out

Many thanks, very helpful. Will have to tell my neighbour I am not a natural blond...more of a fiery red head...so not so dumb after all, but I do like to check my facts before I counter back so thanks again for the info.

Steady on Andrea, as I've said before it's not the leylandii's fault, it's the people who plant and don't maintain them that are the problem. It's precisely this sort of thing that's given all conifers a bad name.

I have nothing against conifers or any plant of that genus, apart from Leylandii, they are a problem to maintain by people who aren't experienced and they don't smell too good either!! All varieties of plants have thugs in their family and I'm afraid Leylandii are the 'black sheep' of the conifer family in my opinion.
I love conifers and your collection is superb.

Sorry Andrea I disagree, the people who plant them in the wrong place are the problem! not the tree. I have a golden form called 'Gold Rider' planted in my collection, I have to keep it in check every year, and I also have many other plants growing in close proximity to it with no problems.

I agree entirely with Bluespruce, it is the owners responsibility for the management of any tree or shrub, which is encroaching on other peoples property which is being used as a screen for the privacy of both sides of a property i.e. Russian vine, Eucalyptus, Pyracantha, Hawthorn and sadly Elm, which we have now lost.
I have no problem with other large shrubs growing in the shade of Leylandii. It is in small gardens in urban areas where the problem has arisen.

I personally think that these trees should come with planning permission in urban areas and conditions should be attached to ensure they are kept in check by individuals planting them as hedges. I totally agree that it is the person who plants and doesn't maintain fault, but this conifer has caused an Act of Parliament to be passed and neighbours and communities to fall out. Inexperienced people will continue to go to garden centres and plant these trees and the local authorities intervention will cause our council taxes to increase. When overgrown trees are cut back, the trees are left with bare dead patches of brown and it looks awful unlike other conifers and evergreen hedging which allows heavy pruning and will re-grow. I know that experienced gardeners can see past the reputation of these trees, but I certainly wouldn't recommend them to anyone because the cons out number the pros. We will have to agree to disagree on this one.

Andrea, people are the problem! not the trees :o)