You need to factor in what type of hob you have to ensure your choice is compatible.
I would also like to say that much brilliant quality cookware is available second-hand on eBay etc. People will sell entire sets of enamelled cast iron as they've changed their kitchen decor, or items being unwanted gifts etc. With a budget of £180, I would definitely consider second-hand as your money will go really far. If you are already concerned about the chemical toxicity of non-stick pans, I imagine planetary health may also be an area of concern for you? If buying second-hand hand, you avoid being part of the process of your demand stimulating the supply process which invariably involves the extraction of finite resources, use of toxic chemicals and burning of fossil fuels during the manufacturing process, followed by further burning of fossil fuels in the shipping and distribution stage. Best avoided; those unintended consequences of buying new will be at least as harmful globally as ingestion of forever chemicals. Environmentally, a much gentler choice is to buy Kate's duplicate wedding gift off eBay and have it posted from Bolton to Bath.
Stainless steel saucepans last forever, just make sure you pick a handle that'll stand the test of time. Mine are coming up to 30 years old and are still ...stainless.
Cast iron frying pans develop a virtually non-stick patina after curing and subsequent use. I fry crepes in mine with minimal fat, and they never stick. I mean, I fry literally everything in them, and sticking isn't a problem unless I've taken my eye off the ball and burnt something. But the you can use a brillo pad without a second thought.
For stews, casseroles and soups, I use Le Creuset enamelled cast iron, which is great as it goes both on the hob and in the oven. My two oldest casserole pans are chipped, scratched and stained (I found them like that on a wall outside a house 30 years ago when I was a student) but they're still my favourites, despite having acquired a few others since which remain in near perfect condition 20 years on (tagine, a couple of wide, shallow lidded casserole dishes and a smaller pan). Clean up is not an issue.
I recommend hard anodised baking trays and roasting tins by Mermaid. Virtually indestructible and easy to soak clean or scrub with a brillo pad. The non-stick property is down to how the metal is tempered and not a toxic layer of chemicals.