Somewhere on here I have posted about my knurling wizard that engraves knurls on cylinders using a 4th axis on a conventional mill. Not directly relevant to what you ask but while I was researching this I came across a couple of special-purpose machines built for milling things like candy-cane on wood. So just a rotary axis and a long X axis, no Y axis though I guess they needed a Z (up and down). A google search may turn up these again.

As someone said, Mach3 probably best avoided as it no longer has support (yet you still have to pay for a license!). Other solutions have been mentioned above, though depending on the amount of home-brew you're prepared to do you could even use something like GRBL which is free.

Would you aim to pass the tube through the "headstock" or use something like a travelling steady to support the free end near where you are cutting?

This company:

https://cnc4you.co.uk/

are based in Milton Keynes and seem pretty good for components, I've certainly bought motion controllers from them. They make their own machines so can probably give you advice on what to use.

For a 3m Z axis (on a lathe type machine Z is the work rotation axis) ball screws would be a bit pricey I think and you probably don't need that degree of precision, so rack and pinion or even chain drive would be OK. Chain drive used for example on the "Maslow" large format router. I can imagine a long length of rack could be expensive and prone to getting bent in transit, but roller chain is cheap as chips. The Maslow drives the chain with sprockets on cheap DC geared motors that have encoders, so really a servo drive.

Where are you based in the UK? I'm not far from Haverhill Suffolk which has a number of firms making autosport fabrications.