Laptop for college

1. "the best laptop(for under £800) that is light and has a great build quality and a long lasting battery life". That is a tall order indeed. You're going to increase your budget significantly, or lower your requirements drastically. I was going to suggest a refurbished laptop, but even that is going to be difficult to find at under £800.

2. Your friend's HP Omen is a gaming laptop, and the battery life may be "great" for a gaming rig, but for a college student 5 hours is not very impressive, and yes, it's also quite heavy. Most gaming laptops are essentially designed as desktop replacements and therefore make no concessions to battery life or weight.

PRICE:
£800 will buy you a host of attractive laptops running on 8th-gen i7 CPUs, e.g. this £700 HP from Amazon UK:
https/www.amazon.co.uk/HP-15-bs107na-15-6-Inch-Laptop-i7-8550U/dp/B078YHYDNR/ref=sr_1_10?s=computers&ie=UTF8&qid=1538421823&sr=1-10&refinements=p_36%3A9708209031%2Cp_n_feature_nine_browse-bin%3A7472693031

Battery life is listed at 11 hours, which probably means something like 8 in real life. Weight is 1.9kg. Between the 8th-gen CPU, the 8 GBs of DDR4 RAM, and the 256 GB SSD drive this is going to be a significant improvement on your current Acer. Build quality is not market-leading, but this 15.6" HP should be able to see you through college, but be gentle.

BUILD QUALITY:
If you're able to increase your budget by £200, this Lenovo ThinkPad T580 is worth looking at:
https/www.lenovo.com/gb/en/laptops/thinkpad/t-series/ThinkPad-T580/p/22TP2TT5800?menu-id=T580

Starting price is £920 and add £75 to get a 256 GB SSD drive (click 'Customise'). Battery life is listed at "up to 27 hours" although that requires the extended battery pack. In its current version you're looking at 12 to 15 hours. Weight is on par with the HP above, at 1.97 kg. It also comes with a 2K IPS panel, which is going to be particularly useful for a college student. Build quality is very good indeed in the T-series, and this T580 will easily last you 7 to 10 years no matter how much you punish it. Both RAM and storage can be expanded down the road.

Best of luck,
GreyCatz.