Cex is a franchised business, where each shop is independently owned. So you might well find that the person running the Cex shop in one town is extremely helpful when things go wrong, whereas the person running the Cex store in a neighbouring town is a total pain in the posterior. Cex stores also tend to be quite bit dearer than some trusted online sellers.
I've bought loads of stuff from this firm, both for myself and on behalf of others. (Several other ABers have bought from them too, invariably providing positive feedback here on AB):
https://accomputerwarehouse.com/product-category/cheap-refurbished-laptops-uk/
Whenever I've had the slightest problem with anything from that firm (which hasn't been very often anyway), they've answered their phone within seconds, offered to call me back if I was paying for the call and then proceeded to put things right with courtesy, efficiency and profuse apologies.
For 'everyday' computing (rather than for, say, playing the latest super-fast games or for high-end video-editing), the Lenovo Thinkpad T460s UltraBook shown there, at £219, would be an ideal machine.
I also have total faith in the integrity of this eBay firm:
https://www.ebay.co.uk/sch/PC-Laptops-Netbooks/177/m.html?_nkw=&_armrs=1&_ipg=&_from=&_ssn=kelsus-tm
(The laptop that I'm using to type this on came from there).
For an 'everyday computing' laptop from that supplier, I'd opt for this:
https://www.ebay.co.uk/itm/314185350488