500 GBP = 578.921 EUR.
I don't know the prices and situation in GB (brexit and shit), but here in good old Finnnnnland I would probably go for something like this:
https://www.kannettavatietokone.fi/Kannettavat/Dell/WGPH9.html DELL VOSTRO 14 5468 14" 7100U/HD-GFX/4/128SSD/W10P
So yeah, for such a low price, I think you'll have to deal with Intel HD graphics unless you catch some good deal somewhere for a lower end Geforce GTX GPU. This one has Intel HD Graphics 620 GPU. Some info on that GPU:
http://www.notebookcheck.net/Intel-HD-Graphics-620.172256.0.html The only thing that makes me think a bit is that it has only 4GB of RAM (8GB would be preferable even for a laptop), but I guess you can expand it later when you save up a bit more money. Not sure if you could actually get the extra 4GB RAM and still stay in your budget.
Don't expect to play The Witcher 3 (or even Witcher 2) with such laptop, but e.g. older GOG games and many indie games should run great. Just make sure you run newest Intel HD Graphics drivers, to me that made a big difference for game backwards compatibility (ie. that older GOG games ran fine, even ones that I have problems with on e.g. NVidia Geforce).
EDIT: Also, that laptop has only a 128GB SSD so it is not that spacious in case you intend to install your whole game library there, but it should be ok for a few games I guess, especially as you will be restricted to older games or indie games anyway due to the performance restrictions, which will be smaller in size.
Surprisingly that small laptop apparently has a second free bay for another HDD/SSD, so you can also use that in case you run out of SSD space. I guess there is room for another hard drive as apparently the laptop is missing an optical drive altogether. If you need one for any reasom, buy an external USB DWD-RW drive or something. I guess this is the wave of the future, more and more PCs, especially laptops, don't even have an optical drive integrated. Similarly like they don't have floppy drives anymore.