Run a 3 Phase machine, on 240v with start & run capacitors
Okay, this is really a common question in some circles- with the cheap availability of inexpensive metal-working machinery in rust-belt areas, lots of people want to take a Bridgeport milling machine or similar and operate it in their garage or basement. 

There are basically four approaches, each with advantages and disadvantages. 


Replace the \$3\phi\$ motor with a single phase-- that generally seems to be an unsatisfactory option. \$3\phi\$ motors are smoother (less torque ripple) smaller and so on. 
Buy a VFD (Variable Frequency Drive) that can accept single-phase input and output \$3\phi\$ power. Note that not all will do that.. there are three kinds- the smallest ones will generally accept single phase at the rated HP. Some will accept \$3\phi\$ input power and can also run from single phase with derating of the HP. Some will only operate with \$3\phi\$ input power. Note that the ones that take single phase have big expensive electrolytic capacitors inside that eventually wear out. 
Make (or buy) a rotary phase converter. This approach uses a surplus \$3\phi\$ motor, generally rated at more than the motor you're trying to power. It simply idles (nothing on the shaft) and effectively generates the missing phases. Since such motors are often available locally for little more than scrap price, it's a viable option and you don't lose anything in starting torque or running smoothness. The idler motor may need to be started with a rope (gives me the willies) or there are more sophisticated ways to do it. This is pretty much the favorite approach with the metalworking contingent, though with the drop in price of surplus and Chinese VFDs, the second option is no longer out of the question even for the frugal.  
A static phase converter. This is the approach you were asking about, except using your existing motor as the idler. You lose starting torque and HP this way, but it will work. The better methods use a voltage sensing relay to remove a starting capacitor. 


Note that some folks do some research and find that there are ways to convert two-phase to three-phase (eg. Scott-T transformers), and that tends to degrade into a discussion of why 240V/120V power in North American homes is actually single phase and not true two-phase. Let's not open that can of worms, it is NOT a 5th way! 

Now that I've blathered long enough I'm going to point you to some tutorials and suppliers rather than duplicate their excellent information. Also, I know very little of Welsh power, and probably couldn't read the warning labels with 12 consonants in a row. 

Here is an e-Bay supplier of static phase converters. The seller is wnysupply, for when that item expires. At less than $50, even with shipping, it's pretty economical, but he's in the USofA. 

Also on eBay here is a US supplier of rotary converter panels (the stuff you need outside the free/cheap motor). About $220. An installation video from the same supplier here. 

A brief overview of DIY here. A better overview of both static and rotary DIY converters here. You'll find reference to a gent named "Fitch Williams" in much of the information- he has written a canonical answer to phase converters. Here's a thread. Fitch is a great guy and a great engineer, but he's gone through some serious stuff in the past few years and may not be able to help personally. 

Now, since I detect a note of reluctance to jump right into the deep end, may I suggest that you find a local chapter of a club of "Model Engineers" (that's what they're called in the UK). They're generally great guys and, aside from being able to whittle an operating steam locomotive out of bits scrap steel- making tools, to make tools, to make tools, they have a great deal of accumulated knowledge on this sort of thing, and someone will probably help you with the conversion. It's not really that big a deal for someone who's comfortable working the the mains. Here is one lead on that.