What is the best Used iMac for under £150?

2011, 2012, or 2014 iMacs cannot run the latest software. If you want an iMac that can run macOS 12 Monterey you need at least a 2015 or later iMac.

With that said, what is the main usage you will be making of the iMac?

email... web browsing, word processing... 2012 or later models would work fine.

something more demanding such as video editing or DSLR Photo management, you may need something a bit more powerful.

gaming... definitely something newer.

For less than £150 you're looking at a 2010 or 2011 iMacs with 8GB of RAM and a slow mechanical HDD. These models are capped at macOS 10.13 High Sierra, and in all honesty are unlikely to be usable anymore for every day tasks. Too many hoops to jump through just to get functional web browser for those models at this time, let alone other apps.

Link-> 21.5" iMac < £150 - eBay.co.uk

They don’t perform at all with the latest software. None of them are capable of running the current version of macOS.

The 2014 will be able to run Big Sur, but nothing later.

If driven by price, and you decide on a 21.5 inch iMac, be absolutely certain it has a solid state drive (SSD) and not the hybrid fusion drive that is slower than the second coming… Also, since RAM is also not user upgradable in these old 21.5 inch Macs, you should look for one that has 16GB RAM rather than 8GB.

Have you actually found any for less than your max? If you have, consider the source carefully and what you're buying. At that price point, I'd think you'll not be getting much computer at all. Certainly nothing near "modern".

When purchasing a used Mac always make sure to perform a clean install of macOS by first erasing the drive before reinstalling macOS. This is extremely important for multiple reasons:

• You know without a doubt you have a good clean pristine factory fresh OS on the computer (Do this even if the previous seems to have done so just to be safe) -- Best to create a bootable macOS USB installer to be safe in case Internet Recovery Mode (Command + Option + R) is not available or does not work as expected.
• You will know whether the Mac has a firmware lock enabled (return it since you won't be able to remove it without the password which means you won't be able to reinstall the OS or boot from external media or recovery mode).
• You may be able to detect the Mac is still being managed by a previous owner (sometimes may not be able to tell until days, weeks, or months later when macOS pops up a notification about the Mac being managed). This is also bad and not something you can fix as it requires a previous owner to remove the Mac from their management system. May also indicate a stolen computer.

Also, later this year when macOS Ventura is released, it will require a 2017+ iMac. However, the current macOS 12.x Monterey is compatible with an iMac 2015, but keep in mind macOS Monterey is only expected to be receiving security updates until mid 2024. Of course apps will still work after this support is dropped. How long third party app developers continue to support their apps after Apple stops providing updates to an OS varies by the developer.

Depending how you intend to use the iMac, an older iMac may be Ok if you are willing to install and use a non-Apple OS like Linux Mint on it. Linux Mint is a free open source OS that can provide you access to the latest versions of the popular web browsers, but most commercial apps are not supported so you would need to rely on the free open source software included in the Linux distribution's software repositories (some people find these apps acceptable, while others cringe at the thought of them). Using Linux is not for everyone or every workload and it does require learning a new OS. However, you still need to mind the dangers of the older computers as the others have mentioned since those older systems are likely using a slow spinning hard drive that is most likely worn out or failing. It is not easy to have the internal drive replaced on the iMacs.