Are you looking for a prebuild or build it yourself ? In either case you are in a difficult situation.
If building yourself.
First thing to do is to install Telegram and join the FEpartalert channel. This will send you an update when the Nvidia Founders Edition (FE) cards come into stock. You will want to get a 3060ti , that is the best card for the money by a country mile, nothing comes close to a 3060ti FE for £369 in terms of value.
Then match that card with the something like this.
My basket at Overclockers UK:
You can pick any case you like and cooler is changeable as well. Windows not included but Win10 is actually free , download the installer from Microsoft website onto an 8bg USB stick and you are good to go. May need a case fan or 2 as well.
Other option is to go for an AMD APU such as the Ryzen 5 5600G
My basket at Overclockers UK:
Once again no windows in the build but this is substantially below your budget and you can add it if you like. Can upgrade many things within your budget so get the case you like. If you were to get a gpu at a later date you could easily add it to this system. With this being an APU with a CPU+GPU on a single die it would not have anywhere near the graphics performance of the 3060ti from the above build. Also 5600G is out of stock in a lot of places so you would have to shop around to find one. For reference the 5600G has similar performance to a GTX1030 or half the performance of a GTX 1060 6GB
When Intel get around to releasing the more value orientated 12th gen Alderlake chips then the 12400 with a B660 motherboard will be the best value option but they are not available at moment.
Looking for a decently priced second hand GPU like Jay85 advices is also an option. GPU is the hardest part to get at the moment.
