https://uk.pcpartpicker.com/
That may help. Sometimes you can find USED parts as well.
THIS GPU is 140 pounds so if he needs a CPU and/or other parts it might be ideal:
https://uk.pcpartpicker.com/product/7Ks8TW/gigabyte-geforce-gtx-1050-ti-4gb-video-card-gv-n105toc-4gd
Here's how it compares to other cards (assuming a good CPU so as not to bottleneck things):
https://www.techpowerup.com/reviews/MSI/GTX_1050_Ti_Gaming_X/27.html
It will run CSGO and LoL very nicely when paired with a good CPU and 8GB of system memory.
If you require a new MOTHERBOARD/CPU/Memory combo as well then probably an i3-6100 is the best choice within this budget. For example:
i3-6100:
https://uk.pcpartpicker.com/product/hV7CmG/intel-cpu-bx80662i36100
Motherboard:
https://uk.pcpartpicker.com/product/MmkwrH/asus-motherboard-h110ma
DDR4 memory:
https://uk.pcpartpicker.com/product/dwhj4D/corsair-memory-cmk8gx4m1a2666c16
I think that is just over 350 pound (for 1050Ti, i3-6100, motherboard and 8GB DDR4 stick) before tax/ship but it's just an example. With the budget motherboard having two DDR4 slots I used a single, fast stick so it could add another 8GB if needed.
I think Windows 10 is transferable but that's a bit confusing.