I have a large garden (by urban standards) with plenty of mature trees, quite a lot of which are self propagated laurel & holly. So I have a chainsaw, but I only use it for the larger items. If I am cutting through a branch / trunk that is c. 4" (100mm) or less I would use a handsaw.
BTW, 40-50mm is in lopper territory rather than saw, Did you mean that?
If you are only going to use it a few times a chainsaw seems a poor investment. It will cost at least the £100 that
@Stivino mentioned (I paid more than that),
plus to use a chainsaw safely you need to spend a lot on PPE; gloves, mask, ear-defenders, boots, trousers.
Where I would disagree with
@Stivino is that I think you need to spend more than £15 and that a bow saw may well not be the best option. I have (the older version of) this
https://www.amazon.co.uk/dp/B00GHDMV4M/
plus handles of various lengths (sold separately) and it is better than any bow saw I have ever used.
Other people have talked about Silky saws in similar terms. I have never used one so I can't comment.