Uh buddy, im in london too (zone1). Am moving out in 3-4 weeks. Want my place? Pretty large room in 4man flatshare in closed gate community. Space that fits my desktopPC 2 monitors and a second table with laptop and stuff. Im even thinking of leaving my desktop PC and at least 1 monitor here in case you are interested.
As for the linked laptop. No, that thing wont run very well. Your investment should be at least 800 as you said. But could easily double if you want something that really does the job. I got myself an Acer predator for christmas from germany (around 1500 pounds) and that has been steamrolling my ue4 and maya stuff with ease.
If theres anything where I wouldnt be greedy/trying to save money, its when getting a decent machine for my work. You gotta see it as an investment.
If you check https://docs.unrealengine.com/latest/INT/GettingStarted/RecommendedSpecifications/ youll find they require a dx11 compatible gpu. So no onboard BS. Get one with a dedicated card, 960, 970, 1060, something along those lines. Also get AT LEAST 8gb ram, 16 is better tho to be safe. And I wouldnt settle for anything less than an i7 cpu.
Also yeah, fullHD 1080 screen is very important as UE4 UI kinda sucks on anything lower. As for storage space, try getting at least 256gb ssd for nice speeds (more of a luxury tho)