What's something incredibly useful you can buy for roughly £100 or less?

i had bought gas stove called firemaple fms, and its amazing, i always bring it to my camping trips, even to some festivals. Its quite compact

A multimeter

you can get a basic oscilloscope for that. aliexpress sells $10-15 multimeters.
- True, but I'd wager a lot more people have uses for a multi meter than an oscilloscope. If you're interested in DIY electronics by all means get an oscilloscope (since you probably already have a multimeter in that case), but if you just need a basic tool for when you occasionally venture into the arcane world of electricity (checking a battery, checking if an outlet is live, checking if a fuse is good, checking if something's shorted, etc) then the $10-15 Aliexpress multimeter is enough. In fact an oscilloscope is less useful to most people because it only detects waveforms (and by extension voltage in general) but not resistance or current among other metrics (unless you get one of those cool combination multimeter osciliacopes).
- $10-15 is still less than £100.

It's a bit dull but having the $100 in your pocket in case of emergency is pretty useful.

When I travel, I always keep a $100 bill under the insole of my shoe. If my wallet gets stolen, at least I have money for a cab.
- Note to self: steal BarneyPiccolo's shoes

induction stove: you can buy a stand-alone element that plugs into the wall for about that much, and they're faster and use less power than a conventional stove
bidet: a low-end model, at least
multitool: should be able to afford a pretty good one for that budget
cajon: all right, maybe not "useful" per se, but man they're a lot of fun!

A bidet and a multi tool are two of my required items.
The best multitool I've found on Amazon is the Wetols one for only $19, and my bidet is the Samodra for $28.49. Extremely cheap, highly effective tools to make life easier.

Slow cooker/ crockpot. You can make multiple meals with minimum effort.

I spent $100 on a stockpot this year and it's made really enjoy cooking. I do love my slowcooker, its just too small.
- I've found that 7qt is the sweet spot for my slow cooker recipes. A 5qt would work for most of them, but having that little extra space is nice.

£100 is roughly the price point for mid-range bone conducting, outside-the-ear headphones. These rest against the bone next to the ear instead of inside the ear itself. You can get lower end options for more like £45

I cannot recommend these strongly enough!

Your ear canal is open to the air, not plugged up for hours
You can still hear your environment, great for biking/walking/running/not getting snuck up on

Good shout!
I recently bought a pair for about £35 and was expecting low end quality but they are more like midrange in my opinion (I bought a Chinese brand, "Sanoto DG08", so I reckon I saved on marketing compared to the market leaders).
I use them all the time now - cycling, listening to adult podcasts around the house or while cooking without being totally antisocial etc. They are great!
You can get em cheap on Aliexpress. ~$15
My gaming PC is hooked up to my TV, Big screen, surround sound, hue lights synced up to it, it's a pretty nice setup
So I got a set of bone conducting phones for when I'm on discord or whatever. I'd rather have the surround sound for the in-game audio, but I don't necessarily need my idiot friends laughing and cracking jokes in glorious 5.1, so they let me still hear and talk to them while leaving my ears open to the speakers
- I'm sure your bgn is lovely.
I'd been thinking of getting a pair a while ago, but the idea slipped my mind! Do you have a particular brand or model you'd recommend?
I'm getting a bit bored of the short lifespan of wireless earphones, whether its due to battery wear or imbalanced sound levels. I also get sweaty ears from over ear headphones, so this sounds perfect.
- I've got an Openrun Pro 2 after my Openrun Pro started getting a weird rattle after a few years of daily use. It leverages a little speaker tuned to be used just outside the ear more than bone conduction, but the app does let you go to a "classic" mode that relies on bone conduction more. Either way, I'm really happy with it. The one thing to keep in mind is that it has zero noise cancellation, so it's pretty terrible in places like airplanes or when you mow the lawn.
- I've been doing good with an older generation of AfterShokz
  I just now searched NYT product reviews for "bone conducting headphones"
  We recommend the Shokz OpenRun Pro 2 headphones for runners who want to hear their surroundings.1They offer a comfortable design that leaves your ears uncovered, producing more bass and less vibration than other bone-conduction headphones.1The hybrid design handles bass effectively, and may change your mind if you've disliked bone-conduction headphones in the past.1For swimmers, we recommend the Shokz OpenSwim Pro headphones, which have a built-in MP3 player and use bone-conduction technology for clearer sound underwater.2They're also comfortable for extended wear and surprisingly stable during swimming.2Another option is the Philips Go TAA7607, which offers similar performance to the Shokz OpenRun but includes a red LED strip for visibility during dusk training.1

An electronics repair kit, e.g. the ifixit toolkit.

I second this. I've had mine for years, that little tool roll has got all you really need to pry open laptops, desktops, and most electronics other than phones and tablets.
- I third this, had mine for years, magnetic box is great, all the little plastic shimmy things are great. Solid quality.

Pressure cooker. Lets you cook a lot of cheaper, bulk food faster.

A quality double-sided safety razor. Saves a ton on cartridges. About as easy to use once you get used to it.

Used cast iron pans - last lifetimes and can be used for so much. French press - coffee, tea, chicory, herbs, mushrooms ...

Honestly, I can't think of much stuff at a higher piece point that isn't specialized. Useful things tend to be relatively lower cost.

I carried a leatherman for years, but rarely used it. I find an adjustable wrench, picquick, pliers and box cutter more efficient and easier to use.

Although, I really want cool stuff.

If you like your hair on the shorter side, hair clippers.

I’ve been cutting my hair for a long time now, and have probably saved thousands from skipping barbers, as well as been able to cut my hair exactly as I like it, and far more frequently/conveniently.

Seconded - I've been cutting my own hair for about 25 years now, must have saved a fortune. Still using the same clippers.
Same. I bought a second hand set of Wahl clippers for £4 from a charity shop after spending two hours and £5 having a bad haircut done professionally.
That was in about 1992.
They're still going strong and I've not paid for another haircut since, nor wasted a second travelling to or waiting around for one.

Ultrasonic cleaner. Cleans all the stuff that's hard to get to usually. Also great for glasses.

I got a battery-powered air blower after seeing a YouTube video comparing and reviewing them.

I've always joked about how stupid leaf blower are, but I've found this pocket-sized version really useful.

Cleaning out dust from computers, tower fans, etc, it is amazing.

I also have a small dust buster and this blower gets its filter really clean like nothing else can.

Unlike cans of compressed gas, there's no concern about inhaling anything if I use it indoors, or getting frostbite when the can cools.

I bought a "for dewalt" handheld vacuum that also acts as a blower/mattress filler. With the small tip on it it's almost as good as the air compressor for cleaning dust out of the pc. It was only $30 iirc
Yeah, I got one of these for my camera gear, but have found hundreds of other uses for it

Second computer monitor
Immersion blender
Basic tool kit
Fabric shaver

Edited to add:

Clear plastic storage boxes/organizers
For cooking: non-stick pans, MSG

I'll push back on the nonstick pans. Steel pans get you much better sears, are easier to take care of, and last way longer than non-sticks. Even expensive non-sticks will require you to use spatulas made of a soft material and will only last a couple months to a handful of years before the teflon flakes off.
Personally I would save up a bit and get a 9inch, a 12-14inch (depending on hob sizes), and a bigger sauce pan. Would definitely run more expensive than 100 quid but will last much longer.
- Ceramic instead of Teflon is where it's at.
I have a fabric shaver I got for Xmas like 6 years ago and haven’t found anything to do with it. Maybe it’s due to just wearing like jeans/cargos/tshirts? Is it supposed to be used for that? I feel like you need to wear something nicer to take advantage of it.
- We used ours to clear pilling from our couches and other furniture.
- I have a few sweaters, cardigans, and sweatpants that I use them on. Nothing super fancy, but using the fabric shaver helps me look more put together when I wear them, even though I’d rather not have a need for the shaver in the first place :)

My leatherman was a little over a ton, and is probably my most used tool. It’s my first line of problem solving in almost all situations

A multitool is a necessity, but Leatherman tools are so ludicrously expensive that it's insulting. Amazon has a great one by Wetols, that has lots of options, is built out of heavy duty steel, has an easy blade locking mechanism, a case with driver bits, and even has the blades on the outside, so you don't have to open it to use one.
Easily the best multitool I've ever owned, and it is only about $19.
That thing must be huge!
- Nah not really, but it comes with a belt pouch though. It’s a little bit bigger than say a boost or a double decker or whatever, and it’s definitely heavy, but not spiky or awkward to keep in a pocket

Or dollars, or Euros, or whatever your currency is

I understand what you mean, but the value of 1 of a currency depends a lot on the currency. 1 euro/U.S. dollar is roughly equivalent-ish to 10 Swedish krona or 100 Japanese yen/en.
- If only there were rates one could work out how many of currency x could be exchanged per dollar.
- Don't worry, it's not a hard rule. Just anything that you would consider to not be super cheap, but not super expensive either.
Yen.