To answer Finnian's question directly (perhaps he wants to make several cylinders over a period, and doesn't want to rely on someone else):
Almost any mini-lathe will do the job. It could probably be done on a Microlathe (Seig C0 size), but I'm prejudiced against them – too small.
Cheapest way in the UK, not sure about Eire, is to order a mini-lathe direct from China. I wouldn't because of the hassle if the lathe turns out to be faulty, and because there's more risk it might be. Read the small-print, chances are you will be required to return a faulty machine at your cost, and this will be ouch expensive. The other issue is that some cheap machines are seconds or factory rejects. Safer to buy from a local vendor who you can talk to, preferably one with a reputation to protect.
You don't need an expensive mini-lathe – these have useful additions like hardened ways, more accessories, and brushless motors not needed for a simple turning job.
All mini-lathes I seen advertised come with a 3-jaw chuck, which is what's needed to hold the cylinder.
My advice, even though it's not critical, avoid very cheap. Something mid-range, about £500.
Brass is easy to cut dry, but don't get the swarf in your eyes!!! Aluminium isn't difficult provided you avoid the alloys that don't machine well. (For example the alloy used to make window frames is intended to be extruded. As such it's soft and sticky and it machines badly, yuk.) Other alloys are intended to be machined and are good to work with. Aluminium needs to be lubricated during cutting with paraffin or WD40 – splash it on with a brush.
An ordinary HSS RH Knife will turn the cylinder down to size. Likely you also need a LH Knife to 'face-off' the ends of the cylinder. 6x6mm or 8x8mm tools will fit the lathe, note they have to be shimmed so the cutting point is at the same height as the cylinder's centre. Occasionally mini-lathes come with a set of cutting tools, usually you have to buy them separately. Strictly speaking, you need a grinding wheel to keep HSS knives sharp. However, provided you don't let them get too blunt, they can be touched up with an ordinary oil-stone.
You could buy a parting tool to cut the cylinder off the stock. However as 'parting off' is quite difficult, especially on a mini-lathe, I'd hacksaw the cylinder off in a vice and return it to the lathe to be faced-off cleanly to size.
120mm is getting on the long side to be turned without support at the tail-stock end. But, with care you should be OK. If you can't hold the diameter (the lathe cuts a taper because the work bends during cutting), ask again.
For both Brass and Aluminium I'd run the lathe at about 500 rpm and take approx 0.2mm cuts. Experiment for best results.
Dave
Edited By SillyOldDuffer on 05/03/2019 10:26:43