Availability of pure alcohol in the UK (or alternatives as fuel for alcohol-burning cookers)

You can't use methylated spirit to cook that way. Methylated spirit contains 1% pyridine to deter people from drinking it, and it will taint the sausage (and no, they don't say what is in it on the label).

The way that excise tariffs are set up, you could buy pure alcohol in UK, but the duty would drive the price to about £75 per litre.

Better to buy pure alcohol in countries that are used to selling it retail (I always bring back a couple of litres from Italy, about €16 / litre).

What you are after is commonly called Methylated Spirits, or Meths. Also known as denatured alcohol

It is made from ethanol (ethyl alcohol) and tainted with a dash of methanol to make it unfit for human consumption. It is usually coloured purple

In many countries it has a bittering agent added (check the label, or taste it), since many people seem to want to risk drinking methanol

The bittering agent may make your food taste very bad with such a cooker you pictured

What you need is "Industrial Methylated Spirits" from food product, paint or chemical suppliers. It generally does not have bittering agents or colouring added, just methanol

You could try getting some Irish Poitín, which is 180 proof, however, I don't know if it's legally sold in the UK. It is carried in the duty free stores in Heathrow and on the ferries to Ireland, though.

You can get laboratory grade, additive-less grain alcohol from here, however, it's £27.98/L + duty (and I think the minimum order is for 2.5L). I don't know if I'd trust something that wasn't explicitly listed as "food grade", though.