The Dell XPS 13 is the current king of the hill. Amazon has it for £850, so perhaps you can find it on sale for less than £800. Most people consider the 1080p display version to be better than the QHD+ version, as it gets substantially better battery life and the increased screen resolution is not very useful on a 13.3" display.
I like the Asus Zenbooks. My first choice would be a Macbook Air but OK if I can't have that, a Zenbook.
Fair warning to the Macbook fans - the Macbook Airs use a mediocre TN panel with middling resolution and crappy color gamut (about 60% sRGB). Resolution is especially important on the Macs because they don't support subpixel rendering. That's why Apple had to move to high-PPI "retina" displays, while Windows PCs did not. https/www.grc.com/ctwhat.htm
The Zenbooks use 1080p IPS panels with 90%-100% sRGB color gamut. They'll come close to or match the quality of the retina displays in the Macbook Pros, and the difference in PPI is not as noticeable because Windows does subpixel rendering. Unless your software ties you to OS X, the Zenbooks give you better quality for less price than the MBAs.