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A somewhat official page about the west highland way states that

The most convenient [cooking gear] is probably the camping-gas variety. Make sure you carry a spare cylinder of gas, although replacement cylinders are readily available en route.

I really doubt I can bring any cooking gas in my carry-on baggage. :-) Gas cylinders come in a variety of sizes and formats. What kind is readily available?

EDIT: I don't actually care if it is propane or butane. The question is mainly about the mechanical compatibility of gas container and burner.

For small gas cylinders for camping stoves, the main question is the fitting on the top. They all contain a similar sort of fuel, usually a mixture of butane and propane. Some may have different proportions of these, but it doesn't make much difference, except in really cold conditions.

Probably the best and most common type is the resealable, screwthread canister. These are available from a variety of brands, eg Coleman, MSR, Jetboil, Primus etc. This is sometimes described as the EN417 standard. The stove just screws onto the top of the canister, and can be easily removed if necessary. These are available to buy in most outdoor shops around the UK, and should be easy enough to find along the West Highland Way, eg in convenience shops or at campsites etc.

There is also the older, piercable canisters. Most common is the Campingaz brand. These were more common, still pretty widely available, and usually cheaper than screwthread canisters. But the big disadvantage is they cannot be resealed. So you can't remove your stove from the canister, until the canister is completely empty. This is a lot less practical for hiking, if you want to pack your stove in your bag each day.

There are a few other types of fittings available. eg the Campingaz "Easi Clic" system. This is resealable, and the fitting looks similar to the screwthread fitting. But it doesn't have a screwthread, the stove just clicks on. So it is only compatible with Campingaz stoves, probably best avoided.

Most places will stock some form of Butane/Propane mix, either Campingaz or a similar fuel from another supplier. You should be able to pick up the small disposable canisters from most outdoors shops, most petrol stations, and some other stores. Larger places should also be able to do you a replacement big refillable canister. When people in the UK talk about "camping gas", they almost always mean the Butane/Propane mix that is sold by Campingaz as that's what they used to be called.

Primus kerosene is probably available in many places stocking butane/propane canisters, as will be methylated spirits.

If you search for either "gas stoves" or "fuel" on the websites of one of the main UK camping stores (eg this or this), you'll get pictures, more details etc of the kinds of fittings and sizes commonly available.

There's nothing on the site to indicate the existence of any "offical" shops or what have you. As such, I can only presume that availability of gas for stoves will be from the stores located on the various campsites you can use en route, and any other outdoor shops you may encounter along the way.

Last time I stopped by any such place, gas from either Camping Gaz or Calor Gas brands was the most common, with big cylinders for caravans and the like, and smaller camping cylinders. I realise this isn't massively helpful with regards to knowing what fittings to use.

You could investigate what stoves and fittings are most common on major UK outdoor retailers (try Blacks/Millets, GoOutdoors and Cotswold Outdoors). If there's some commonalitiy, you will probably be able to get refills for this most places.