When I was a kid and was still living in Poland, my parents used to have these few kilo rechargeable gas bottles and compatible stove, which we used during holidays. The nice thing about this was that the gas containers could be refilled in LPG equipped petrol stations for the same price as the gas used in LPG converted cars (so a tiny fraction of the cost of the backpacking gas containers popular today). Is it possible to buy these kind of stoves in the UK?
Upfront I would like to mention that I don't live in the UK, but I hope my answer is still relevant.
The most commonly used stove brand in the US is Coleman, and I looked on amazon.co.uk, and it looks like they are common in the UK as well.
For Coleman camping stoves you can buy adapter cables to connect them to large, refillable propane tanks. The common size in the US for those tanks is 5 gallons and you would use this kind of hose (us amazon to 5 gallon tank) to connect a propane camping stove to a refillable tank. Something like this (UK amazon) might be something you need instead.
An alternative approach is a liquid fuel stove (UK amazon). You can refill these with camping gas or regular unleaded gasoline, which makes it a little more versatile. A word of warning: these stoves are a little more involved; you need to manually maintain pressure in the fuel tank by pumping, and you need to prime the stove before you use it (A procedure that is not very difficult and takes about a minute.) I really like liquid fuel stoves, my wife prefers propane. We have both.
Let us know if this worked for you in the UK so we can reword the question and answer so they are not just specific to the UK.
I know very well the Polish LPG small butane/propane cylinders that Polish use for their camping stoves and gas lanterns. They are unique because they are small and they are legally refillable by individuals in an LPG car pump. The Polish cylinder comes with an Italian/French/Polish adapter for refilling at the LPG car pump and the cylinder has a special security valve to avoid over-filling (fantastic idea!). I have seen them in Lithuania where they have been very popular for decades for outdoors. They are also unique because they have a thread that is unique to them and you can only use Polish and Russian camping appliances (lanterns, stoves, heaters, etc.) made specifically for the typical Polish cylinders.
First, in the UK and in all Western Europe it is illegal for individuals to refill an LPG cylinder in an LPG car pump, because car gas, heating gas and camping gas are taxed differently. HMCR prosecutes people who sell or buy LPG in a car pump and use it for other purposes than transport. The same happens in the other countries in Western Europe. That makes the Polish gas cylinder concept very attractive, but very difficult to apply in Western Europe. This is the reason I did not buy one myself.
In Western Europe, we have the equivalent small camping cylinders, but they are not refillable by individuals at the LPG car pump as they are in Poland. They are exchanged by the distributors when they are empty, by a new one full of gas that is taxed appropiately (expensive). The most popular and similar cylinder to the Polish refillable LPG cylinder are the blue French butane refillable cylinders of the brand Campingaz (only available filled with butane, not propane). They are availabe in all the tool shops and camping shops of Western Europe in the same sizes as the Polish refillable cylinders. There are plenty of camping appliances to specific for them (they have a specific thread to them). Bear in mind that refillable Campingaz cylinders have no security valve to avoid overfilling, because they are not designed for refilling at the LPG car pump.
Campingaz also makes diposable blue combined propane/butane canisters that are littered when emptied and there are also many camping appliances for them. They also have their own different special thread for Campingaz camping appliances, but they are available in all Western Europe too.
Campingaz, although originally a French company, is now the property of Coleman, the US company. Coleman has it own disposable camping propane/butane canister with their own type of thread too and they plenty of camping equipment available for them. The Coleman thread of disposable propane/butane canister is used by other outdoors brands like Primus, Optimus, etc too. The Coleman propane/butane canister type of thread is the most popular thread in the United Kingdom! In the UK it is the one you find everywhere and it has plenty of applainces of plenty brands available. They are also available in all Western Europe and in the USA.
Campingaz, both the disposable propane/butane canisters and the blue refillable butane cylinders are the most popular threads and gas in France and in the countries the South of Europe, but Campingaz is not available in the USA. The truth is that any good outdoors shop in Western Europe will have the three systems I have described: Coleman thread disposable canisters, Campingas thead disposable canisters and Campingas refillable cylinders. But in a supermarket you will only find the dominant model depending of the country where you are. If you plan going camping to a beach in the South of Europe do get Campingaz refillable cylinders.
Finally, the USA has the Coleman popane only disposable cylinders with American thread. They are the only propane only cylinders in the market. They have now started to sell in the UK, Netherlands, Belgium and Germany, but even in those countries its distribution is still scarse. They are the best option for Winter camping. They are not available in other Western European countries yet.
The national petrol company makes its own cylidners too (Calor in the UK, Primagaz in France, Repsol in Spain, etc). This is only available in those countries and they are not popular among outdoor people because they are still too big and heavy comapred to a Campingaz blue refillable cylinder.
Some petrol stations have a stock of LPG canisters outside, which I'm pretty sure are meant to be returned to be refilled - these are known as 'Calor gas' after the name of the dominant company in this market. They go from about 5kg upward, which I guess is quite large. I've never bought one, so am not sure how you'd go about it. Check which type of gas regulator you have, as I believe there are at least two different types.
A mate of mine swears by the Trangia stove, which is fuelled with methanol. Methanol burns clean and is probably safer than LPG. They're pretty common in camping shops here. The fuel is a little harder to come by and goes by the name 'methylated spirits', which you can buy in DIY shops. 'White spirit' is not the same thing as it is a petroleum byproduct, and would probably produce a smoky flame.