If you're contemplating stir-frying, a wok is a natural choice. I've used a 14" Taylor and Ng wok for years and years and liked it a lot. It has a stick handle with helper, and a flat area on the bottom. My nephew asked for a wok last Christmas. I went to a large Asian restaurant supply house to see what they had. They had plenty of big big woks, with metal loop handles, and the full wok bowl shape. The traditional wok shape has lots of reasons for being, so that wasn't a deal-breaker, but I do prefer the stick handle, so I looked online for the exact same wok I had, and got him that, even though it was quite a bit pricier.
I spent quite a bit of time in China in the 1980s and 1990s. Generally, they used spun steel woks. The woks were placed on coal-fired burners with a round opening at the top. The bottom of the wok fit into the opening, so a good portion of the wok is exposed to the extremely hot coal fire. The bottom of the wok would literally get red hot.
That being said, what we might know as a "dish" or one plate of food was usually done one at a time. The really big woks were used for larger portions of various things (like, say, deep-frying a big batch of sesame balls), but not so much for individual dishes. Same thing, if you're cooking a stir-fry at home, if you fill the wok up with a whole lot of food, you're going to end up steaming it more than stir-frying it.
In my own cooking, usually for three or four people, quite often I'm doing things in batches. For instance, one of our common meals is chao fen, or fried rice noodles. I'll cook the noodles in a stock pot and put them aside. I'll soak shitake mushrooms, and then make a sauce with the mushroom water. I'll then braise the tofu in a 12" cast-iron skillet (more on that below). And then I'll cook vegetables- baby bok choy, shitake mushrooms, onions etc- in the wok. Then to serve, I'll heat up the wok hot hot, add some oil, measure out a bowl of noodles, throw them in, then portion out a serving's worth of vegetables/sauce/tofu, and then stir to combine. Repeat for each eater.
The killer set-up, presumably, would be to have a very high-BTU wok burner. They make stoves that have a burner like that- high BTU and shaped to accept the round-bottom wok, combined with other regular burners. Maybe when I replace my current stove! There are also stand-alone wok burners that run on a tank of propane that can be used outside. I might try one of those sometime, to better get the desired "wok hei."
At any rate, it is worth keeping in mind that how big you can go (on the pot) depends on how hot you can go (on the burner).
As I mentioned, I also have several 12" Lodge cast-iron skillets. I use these ALL the time.
My stove is gas, with a respectable output. Where I used to live, I had a stove with a HUGE output. I was sorry to leave that one behind. Anyway, for my setup, I don't think a skillet larger than 12" would be better. It's just hard to get the heat all around when the skillet is so much larger than the burner, as others have mentioned. I find two big skillets very handy, though. For instance, if I'm making migas (eggs, tortilla strips, onions, jalapenos, tomatoes, cheese), I can toast the tortilla strips in one skillet and do the eggs and onions in another. Or, if I'm making burritos, I'll have the filling in one skillet, and warm the tortillas in the other.
I've used stainless skillets (e.g. All-Clad) at other people's houses. Not my bag. In my experience they stick like a mofo. Give me cast iron or carbon steel all day long. Even for eggs. Even for tomatoes. YMMV.
I'd suggest finding your nearest Asian restaurant supply, if you've got one at all locally, and just getting a wok. Either a round-bottom on with the separate ring, or a flat-bottomed one. I can't speak to what sort of cast iron you might have available in the UK, but if you've got decent heat output, I would think a 12" skillet (or two) could be the bees knees. I like my Lodge just fine, but if I had to do it over again, I might opt for one of the more "boutique-y" skillets. Cry once, you know... you're amortizing that sucker over years and years and years of use. My oldest 12" cast iron skillet is 34 years old, and I also use a smaller 6" one that was my great aunt's. It was made in the 1930s.
