I want to buy a gaming laptop for maximum £700 which I know won't be that powerful but I want it to be decent to be able to play Diablo 3 and CS:GO. I don't play high - end games like Far Cry, The Witcher etc.
I like the second one because it is more powerful but I read some reviews about PCSpecialist and they said that they are not very good because computers are often missing parts or not working properly.
Oh no! That doesn't sound very promising! Ebuyer are an excellent company though. They would deal with any problems very quickly. I bought an Alienware laptop 4 years ago and it is still going strong so if you can be patient and save up a bit more money, I'd definitely recommend them. You can also try to find a second-hand one. My M15x can score P7246 in 3Dmark 11 https://dl.dropboxusercontent.com/u/2654032/P7246.jpg
You'll struggle to get anything more powerful than a GTX 760M at that price point apparently. I did find an MSI laptop with an A10 APU and a 8970M but I can't recommend AMD mobile chips because they are awful.