Honestly, it's not always "the fence on the left".
When visiting to discuss potential boundary disputes, if there's one urban myth we hear more than any other, way more, it is this one:-
" you always own the boundary on the left and so it's my fence".
Sorry, it is just not true. Really, really, really believe us on this one. This myth causes so much anxiety between neighbours.
Firstly, do not think of it as "owning" any boundary. Think of a boundary as being invisible, just a legal function to explain that the bounds of a property has a limit, where one property ends and the next starts. There might not be anything there at all to physically "own" (such as with 'open-plan' front gardens).
If there is a fence or hedge (or other feature) between the gardens then it might be written somewhere as being the responsibility of one property owner or the other to maintain that as a marker of the position of the legal boundary.
Which then brings us, secondly, to do not assume that the fence or hedge (or other feature) that you can see is the feature that is referred to in old documents. It could well be that an old feature fell down and a new one put up in a slight different location.... that does not necessarily "move" the boundary with it. It might just mean that there is a fence or hedge that is no longer at the boundary. So, in-turn, that means the feature might not be on your land and so not yours to touch.
So, if it doesn't say it in any of your Property documentation then you cannot just make the assumption that the fence or hedge is yours, just "because it is on the left" (or other position of any other myth).
You need to be looking for other evidence or indications, you need to be looking at documents, you might then want to be taking professional advice to avoid a dispute based just on an urban myth.