Going by your details, I've found these 3 machines:
From John Lewis, there's this £750 Dell:
https/m.johnlewis.com/dell-inspiron-15-gaming-laptop-intel-core-i5-7300hq-8gb-ram-1tb-hybrid-hdd-geforce-gtx-1050-15-6-inch-full-hd-black/p3417501
Saveonlaptops have this £700 MSI:
https/www.saveonlaptops.co.uk/9S7-16J962-1868-MSI-GL62M-7RDX-1868UK_2271328.html
And Amazon UK have this £629 ASUS:
https/www.amazon.co.uk/ASUS-Vivobook-A556UQ-DM1469T-15-6-inch-Processor/dp/B078JXYH21/ref=sr_1_4?s=computers&ie=UTF8&qid=1522178448&sr=1-4&refinements=p_n_style_browse-bin%3A182753031%2Cp_n_pattern_browse-bin%3A937175031%2Cp_36%3A60000-70000
The Dell is £50 over budget, but it comes with the larger 4GB 1050 GPU. Like the MSI below it's a gaming machine so battery life is virtually nil, and you have to supply your own external Blu-Ray disk drive. Overall the specs are pretty good - quad-core CPUs and GTX 1050 GPUs. The Dell adds an 8GB SSD partition to speed up boot times - the MSI relies solely on a mechanical drive. The Dell allows for serious gaming, while the smaller 2GB 1050 GPU in the MSI will require some adjustments to game settings. The MSI comes with an IPS panel which will improve portability much more than the other 2.
If you can make do with a dual-core machine, the ASUS Vivobook will offer significantly better battery life. It also comes with a built-in DVD drive. The 2GB 940MX GPU is designed for movie watching and fancy business presentations. I would consider the ASUS the one to get in your situation, but the MSI is a very attractive alternative.
Best of luck,
GreyCatz.