I would like to but I don't feel familiar with british websites that offer gaming laptops for a good price so I suggest you to intestigate where to find cheap laptops so then
I can select one from the site.
But it's not that difficult to choose one as you have no much money, so the only thing that really matters is a decent GPU. GDDR5 if possible maybe a GTX 950M, 860M, GTX 850M or any other GPU with similar performance. If the money isn't enough grab an R7 M260, GT 940M, etc. Here you can check a laptops GPUs ranking:
http/www.notebookcheck.net/Mobile-Graphics-Cards-Benchmark-List.844.0.html
It's the only spec you should really consider due to with 300gbp no one will offer great features.
If it's possible try not to get a big laptop a good size is 15.6 which is pretty common in any laptop. And a laptop that comes from a good brand such as ASUS, lenovo, dell, toshiba, MSI, gigabyte, etc.
ACER and HP are not good brands at all and you can elect them for being cheap, however you really requiere to take care of your CPU and GPU temperatures by using HWmonitor and even getting a base with fans.