Looking to buy a decent laptop in the UK on a small budget

Games that I assume are low on requirements like Nightsky, Puddle, Mark of the Ninja. Please feel free to correct me if I'm wrong assuming they don't require too much.

Basically, I understand not to expect miracles for a system on a low budget. I'm obviously not expecting to run Bf4 or the newer cod series, but I'd like to be able to play some basic games while sat on the sofa.

You're correct on that. The AMD Radeon HD 8240 is also an integrated graphics (not a seperate GPU) with certain AMD APUs (E1-2500 in this case). Both the Intel CPU and its integrated graphics, Intel HD Graphics 4000, is superior to the AMD E1-2500 and its AMD Radeon HD 8240.

First, here is an example of a benchmark between the two (still looking for more):

AMD Radeon HD 8240 (282 points)
Profile of AMD Radeon 8240 (bottom has baseline score for the latest 5 tests with the benchmark)

Intel HD Graphics 4000 (457 points)
Profile of Intel HD Graphics 4000 (bottom has baseline score for the latest 5 tests with the benchmark)

3DMark (2013) - Ice Storm Standard Graphics 1280x720:

Average score:
AMD Radeon HD 8240: 25296
Intel HD Graphics 4000: 31489.3

3DMark (2013) - Cloud Gate Standard Graphics 1280x720

Average score:
AMD Radeon HD 8240: 2273
Intel HD Graphics 4000: 3701.5

3DMark (2013) - Fire Strike Standard Graphics 1920x1080

Average score:
AMD Radeon HD 8240: 290
Intel HD Graphics 4000: 484.8

You can compare the rest of the benchmarks between these two pages (Intel HD Graphics 4000 seems to outscore the 8240 on all the benchmarks):
Notebookcheck - AMD Radeon HD 8240
Notebookcheck - Intel HD Graphics 4000

CPU wise the Intel Core i3 3110M outperforms the AMD E1-2500 - Higher clock speed (2.4 GHz to 1.4 GHz), hyperthreaded (not really relevant for gaming), has more threads (4 to 2 - can benefit CPU heavy games like RTS with lots of calculation and AAA RTS can use 2-4 threads) - and better integrated graphics.

Intel Core i3 3110M vs AMD E1-2500 - CPUBoss

By the looks of it, the Lenovo G500 seems like a really good choice for a 300 pound range laptop at the moment.. It's discounted a good chunk from 370 to 300 pounds. It should be able to outperform any laptop with a baseline 300 pound price as it's more belonging to the 400 pound range in terms of performance. I haven't been able to find a better one at 300 pounds.

Disclaimer: I am by no means an expert in this and my post may contain things that may be wrong. Feel free to correct me anytime.