I own a mid-high range Gaming laptop since my work requires me to move around quite a bit. It's the ASUS G75VW-DH72:
http://www.amazon.co.uk/ASUS-17-3-Inch-1920x1080-i7-3610QM-Quad-Core/dp/B007MW73C2 (UK Link for you!)
In terms of a desktop replacement it is still very up-to-par even with their latest model, the G750. While the processor and graphic card are mid-range, the 256G SSD and Bluray reader/burner is quite a bit of a draw. Even with these specs I don't have much trouble playing most recent games at 1080p (which shows really nicely on a 1080p native screen). If you want a relative comparison I can run The Witcher 2 at 1920x1080 at a constant 45-50 FPS, with Ambient Occlusion and 2xAA. The SSD allows for really fast load times for any multiplayer games you want to install, and allows for a 5 second boot up for your operating system. It includes a 750 GB SATA 7200RPM SATA HDD as well for storage. It has very powerful fans as well, which is a function that most laptop purchasers overlook. Since the bane of every laptop's existence is overheating, which can drastically reduce the lifespan of all of your hardware components.
Also if your situation allows for it I STRONGLY advice that you build your own desktop computer. I own one as well, except I just don't get to use it as much as my laptop. The general rule of thumb being that if you want to play video games, investing in a custom Desktop is almost twice as cost efficient as investing in a laptop, and infinitely times more future-proof since you can update your hardware every few years (whereas a laptop you just chuck out).
For a relative price-performance comparison visit this site:
http://www.logicalincrements.com/There's even a dropdown menu for your country to get local pricing. But the main usefulness of this website is to give you an idea of how much a state-of-the-art Desktop computer will cost you, and each "template" lists all compatible parts, so you don't run the risk of buying incompatible hardware.
My desktop computer, which is in the range of a "Exceptional" gaming PC by that website's standards, runs every single modern PC game at Very-High to Ultra at a constant 60FPS. Which is quite a bit of a waste of money, but I'm hoping that it's future-proofed enough to run the Witcher 3 or some of the higher tier Korean MMOs whenever those come out. Realistically you would only need a "Great" gaming PC to run all modern games and have them all look exceptional.