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I only own a hacksaw for bike jobs but this weekends lockdown job is, hopefully, cutting a small ish holly tree down.
However, I have no idea what type of hand saw I'm best to buy, so advice appreciated. Ideally something I can get on Amazon Prime. And I won't be buying a chainsaw!
Axe for the win.
Folding saw if it really is small. Bow saw if it's a little bigger. Or both, they are both handy.
Upto 4-5 inches little folder or rapsaw type thing
Check it for nests, a lot of birds on second broods now
Just been out in the rain and measured the trunk, it's about 5". Bow saw sounds like the way forward, going to order the Bacho one Houns has pictured. Thanks everyone 🙂
thestabiliser hadn't thought of that, good idea!
Roughneck 12" bowsaw.
Will normally do the job of a bigger bowsaw, but will fit in a cycling pack for trail maintenance.
£10 from Toolstation.

I'd go for a decent pruning saw. Easier to handle than a bow saw for smaller bits.
Just get a decent sized blade, eg 300mm. Doesn't need to be folding if its just in the garden. Can still fit it in a backpack for cycling, maybe sticking out the top a bit.
This one looks not bad. https://www.amazon.co.uk/GR%C3%9CNTEK-Barracuda-hardened-3D-Teeth-plastic/dp/B01CP13GCK/
Or a Silky Zubat if you want something fancier. https://www.amazon.co.uk/Silky-Professional-270-33-Curved-Blade-Scabbard/dp/B0014C4QMG/
Silky f180. In my backpack for a little trail trimming after the FC have been in. Makes short work of trees upto about 8" diameter.
I'd agree that a pruning saw will deal with that size and be more useful for gardening jobs in the future. For example I own two chainsaws but still grabbed a punning saw, about 9-10" blade, to cut a 4" branch from a neighbour's oak tree and it didn't take long. Silky are the best, but not the cheapest.
That f180 was £20 delivered.
I'd go for the Silky too. I even managed to use mine at the weekend on the end of a decorator's extending pole to prune some 3-4" branches on an oak about 15 ft up. 75-100mm/4-5m high in work terms...
The humble bow saw an almost perfect tool. Cheap to buy, with replaceable blades available for peanuts virtually everywhere.
What's not to like!
Bow Saw...no question.