Linux

Refurbished Thinkpad. The answer is always refurbished Thinkpad.

Instead of just throwing random preferences out there, I'll help clarify the field of comments:

1. Thinkpads USED to be a safe choice, but Lenovo has been tainting that model line for a few years. Search and find specific models, and don't just buy because it has the Thinkpad brand.
2. Framework is 100% ready to go. They have a Refurb store where everything is cheap, but if you find one cheaper, get it.
3. Dell had a ton of Linux ready laptops under the XPS brand not long ago. Search and find out which to make sure, but they shipped with Linux installed.
4. I hate to say it, but HP Probooks were solid and shipped with Linux also. Terrible company, but they make decent enterprise products. They'll sell for cheap on eBay.

People are going to say Thinkpad but I am going to say 2013 to 2017 MacBook Air. Inexpensive. Light. Good looking. A joy to use. Faster than you think. And well supported under Linux (I use EndeavourOS on them myself).

Used Thinkpad X or T series

The generic answer for this is to get a refurbished thinkpad. Pretty much any T-series fit your needs and there's plenty of pre-leased corporate machines around which are refurbished and often have even a some kind of warranty.

A refurbished Thinkpad T480.

I have recently bought 2 dirt cheap thinkpads, one for me and one for the wife.

T490s - i5 intel
T14s - Ryzen 5 AMD

Both are tick all your requirements except for the numbpad, the T14s is definitely worth the extra money, though. It can even handle some medium gaming.
Both have upgradeable nvme ssds. However the ram is soldered on the "s" versions of these laptops so find one with 16gb or more.

loving my recently acquired T480. not the fastest by any means, but solid and great keyboard. plus non-soldered memory allows for upgrades. got mine off craigslist for 120, a steal.

If you're able to code from a terminal, and care about longer battery life (my main concern when working from a coffee shop or elsewhere), I'd recommend getting a used android tablet, pry something from xiaomi or oneplus. You can find a decent model used for around that price with > 8 hour battery life easily.

Get a good stand, a solid bluetooth keyboard (logitech makes some great portable ones), and put termux on it (can probably handle light python locally).

If you need it to do CPU powerful tasks, use termux to remote into a VPS or your home server, and let a plugged in linux machine do the work so you can save your device's battery life. This is how I code at least.

I've had great results with various refurbished Dell Latitudes from eBay over the years. I have a stack of about 5 or 6 of 'em and they've all run many mainstream Linux distros with fantastic out-of-the-box support. I pass 'em out to members of the household whenever a laptop is needed and they'll usually get the job done.

I'd just type in "Dell Latitude" on eBay and filter by price and such. I suspect any model with an i5 and 8GB RAM oughta be fine for light programming work. I've found sellers with high ratings (like 97% or higher) and thousands of sales are pretty reliable (and tend to have return policies in case you get a lemon). Just test all the hardware (webcam, microphone, headphone jack, USB ports, ethernet, etc) as soon as you get it.

I've saved a lot of money over the years buying secondhand, and these machines have been running without a hiccup for years of casual use.

t480 or t470

If you're in the US, refurbished thinkpads are probably the best option. Not so much here in Australia (but you mentioned GBP so perhaps you're in UK). Whatever. I bought a refurb Dell Latitude 3120 for AU$229

mfg yr 2021 Intel(R) Pentium(R) Silver N6000 @ 1.10GHz 8Gb RAM Intel UHD graphics Intel Wi-Fi 5 9560 (160 MHz) Bluetooth 5.0 Display: 1366 x 768 11.6" touchscreen 2-in-1 Disc: M.2 256Gb PCIe NVME Class 35 SSD 1.35kg

Runs voidlinux like it was born to it. It's my travel laptop.

Dell latitude 14 inch 5430 or similar, cheap ish. Its got all the wants and needs. Plenty of ports. Its dell so it'll survive forever.

maybe search for system76 too. I found one on my local craigslist.

A refurb!

Keep browsing eBay and HotUKDeals. You can easily find something really good for <£200.

This 11th Gen Intel Dell laptop was going to £150 this morning and I was on the verge of ordering it and adding more RAM.

This sub is obsessed with Thinkpads, but when you're looking for a secondhand bargain then you pick up what comes opportunistically. The market is flooded with Dells because businesses change machines long before they go out of date and generally keep them in very very good condition.

I'm not sure how common they are outside Japan, but I have a little (about 12" I think) Panasonic "Let's Note" that I use quite a lot as a lightweight coding (and retro/indie gaming :D) device that I can throw in even my smallest bag when there's a chance I'll have to kill more than a few minutes. They're designed to be a little bit rugged. I had Ubuntu on it previously, now Mint, and the only problem I've had is that Linux somehow sees two screen brightness systems, and by default it connects the screen brightness keys to the wrong (i.e. nonexistent) one. Once I traced the problem it was a quick and painless fix.

They seem to be sold worldwide, so you may be able to get one cheaply second-hand. One thing to be careful about is the fact that in order to keep the physical size down, the RAM is soldered to the board. Mine is an older model (5th gen iCore), and has 4GB soldered on but also one SODIMM slot, so I was able to upgrade to 12GB total. But I've noticed that on most later models they got rid of the RAM slots entirely, so whatever RAM it comes with is what you're stuck with.

A light Chromebook?

intel macbook air works good for me, with debian and xfce

Under 140, latitude 5290 (from 2018, 8350u). I bought it ~2y ago. Small, 12 inch, decent keyboard, very upgradable, decent build quality, but the LCD is horrendous. Edit: used, could probably be found under 100€.