-
established trees do grown back quite quickly.
as others have said, pollarding is best done every one or two years as this reduces the shock to the tree, but many species will tolerate being pruned hard less frequently, and sycamore is one of these.
rough guide, if you were to prune it and leave it, 40% reduction will probably take 4 to 5 years to get back to about where it is now, pollarding maybe 8 to 10 years.
btw looks like there are two trees there, in different gardens, which have grown up to form one canopy?
Edit - just noted that you have said it's two trees in the OP.
Our neighbour have this massive Sycamore in their garden, plus another smaller one in the next house down. It's getting pretty massive and blocks a lot of light to the surrounding gardens. The neighbours are elderly and have been living in the house (renting) for 30 years. I thought I would get a quote/plan and then approach their landlord and other neighbours after that.
I have just had a tree surgeon out to advise/quote. He said it looks like it has been pollarded about 30+ years ago and then not touched. He said he could reduce it by 40% for about £1k or pollard it for about £2k. He recommends pollarding it.
What experience/advice does the hive mind have? I like the tree, I would just ideally have more natural light and have it a bit more under control. Ideally we won't have to spend lots every few years keeping it in check as well.