Hi, I have reduced the height of Leylandii several times and most times managed to get away with it. Firstly, I would recommend that you do not reduce it substantially during the growing period. These are large trees and this type of shock when they are active won't do them any good. If you can leave it until October, that would be better.

I have managed to take about 10ft off 30 foot trees in the past. One died but all others remained. If you have a lot of soft, new growth you can cut into that without doing too much harm. Going back into old hard wood needs more care. If the hedge is a boundary which provides privacy, I would try to achieve a reduction gradually. Star with the new growth and a short trim this year, then try removing a further couple of feet next year. Be careful of cutting into stems which are more than an inch or two thick and I would be wary of chopping them in half in one go!

I'm sorry that this is not more specific, but I think it depends how important the hedge is to you. Cutting back mature trees substantially is risky in most circs.

They grow 3-5 ft per year so if you only reduce by 3 ft-5ft every time you trim you are playing catch up!
If you trim by less than 3ft they will continue to get bigger.
Did you know the legal requirement is 2m for a (Leylandii) hedge? if you continue to let it grow you may be given a notice to reduce it?
The best time to trim ideally is May but most have to be done twice a year anyway. Why not get a tree surgeon in this first time and let them set you up with an easier to maintain hedge?