I have just bought a 1960s terraced house. Something which I didn't notice when viewing (in winter!) is that on one side there is an incredibly large boundary hedge which seems to be made up of leylandii and some other large shrubs. When I say it's big, I mean it is four and a half foot wide! However it is really encroaching into what I think must be my garden because at the moment it is most of the way across my dining room window (at the back of the house), and actually means that for example a window cleaner can't get access to the top and bottom windows on that side. I think what has happened is that some years ago the owner of my house has planted one row of leylandii on their boundary and then over time has planted more layers of shrubs in front of them! I have used a tape measure inside my house to measure up to the wall and then measured the same distance outside and it definitely goes to just after the edge of the shrubs so I think I do own them. I also checked my land registry plan and it seems to just show a long straight garden from the boundary of the house (which would also be on the far side of the shrubs).
I would really like to get rid of this mega shrub (!) and replace with a simple fence: partly because they are taking up four foot of width of my garden and partly because I've got a small child and I think a fence would be a more secure low maintenance boundary. However I am worried about how long this weird boundary issue might have gone on and I don't want to annoy my new neighbours. To compound it, they haven't said one word to me since I moved in (I actually moved at the start of July but have been renovating the property since April) despite my efforts to smile and wave etc. I would ideally like to get a tree person round to have a look and give a rough quote to remove the shrubs/get a fence quote and then pop a note through neighbour's front door to alert them what I'm doing. Would this be ok? Also should I be aware of any other pitfalls regarding removal of shrubs like this in a garden?