Yes, we had Leylandii cut back last year. We did need permission from our local tree officer but because we are in a conservation area so we need tree permission for all trees over a certain size. If you're not in a conservation area, you don't need permission (there's no way they'll have a TPO on them).
We had about 60 to 70 trees cut back by 3m to 5m (the tallest were about 8m and we've taken them down to about 3m). If yours are 30m (which is absolutely enormous - and must be going on for record breaking - are you sure? ETA - just seen your photo, hard to judge but I'd guess closer to 15m than 30m - bearing in mind a two storey house is probably about 8m), taking them down to 5 ft would be a certain death sentence. I imagine they have very little green growth in their bottom 5ft. Also, as somebody says, they are probably there are a wind break and 5ft is not going to stop any wind. If you hate them that much, just take them out. If you can concede a use as a windbreak, 3m would stand a chance of survival and might come back to look decent after a few years of good pruning. Ours still look a bit shabby because they hadn't been pruned for years but I think they will green up more and more, at least on the sunny side.
Ours were burnt on an enormous bonfire that lasted for over two weeks. It required tyres to start it, left ash all over the neighbours windows (wind changed direction shortly after lighting) and was probably not great for the environment but saved paying the guys to take it away. I did use some of the ash around the garden and on the veg beds and yet to see the results but we're on chalk downland so added acidity is no bad thing.
Your cheaper option would be just to have them taken out and then have the stumps ground. It'll still be hard to replant but a row of stumps looks awful. Our way involved men with climbing gear and chainsaws dealing with each and every tree individually so it took three guys a week and cost us over £2k.