-
Refurb would be the way to go IMO. Excellent deals such as this (with a 1 year warranty)
Chuck in an Office365 for Students subscription, job done.
-
The most bang for your buck would be second hand. Either the one that Manc_Ronnie linked or something like this https://www.ebay.co.uk/itm/Lenovo-Thinkpad-X260-Core-i7-6500U-2-50GHz-8GB-Ram-500GB-HDD-Webcam-HDMI-Laptop/323966207690? (I've bought a few laptops from this ebay seller and they're all fine).
These laptops are pretty powerful for the price and a better build quality than what you'd get new in this price range (they're ex-corporate machines so designed to be a bit more robust and long-lasting). The downsides are that they may be a bit cosmetically damaged, the screen resolution isn't always as good and the battery life is rarely anywhere near as good as a new machine (this is partly because the batteries are old, partly because a lot of focus has gone into making computers more power efficient in the last few years).
If you're going new and willing to go up to £500 (well, £516) I would go with this from the Dell outlet store
https://outlet.euro.dell.com/Online/SecondaryInventorySearch.aspx?c=uk&cs=ukdfb1&l=en&s=dfb&sign=PXhcOSHtr1T4IOw%2fPR7UdfPVr%2fBMMC3rhUr6l0wkldUSsQRCCGsfuCb4F9SW2bMz6x8T8tmTqdcVEb0DjDFoA%2fnw%2fzswH0IOjZUBBoeFJC7fda4NNtZOJFJ%2b6QygdKzq49aGRcOEgrlNJytZsInMfVlQr6x%2bkGWyhymf%2b%2fLMh2wgaHcgbXTjSU0Hy74Gyn8FC%2bIWoUsGZizSekZkVlPCN0ipINs0fjDWEw1cVew6SHEBamhU4rCxjsqCfvwWW2HJ9k63GjMbcZA%3dIt's very powerful for the price and the outlet store stuff is basically new. It's a better screen and a way better processor than the second hand ones linked. It also has newer features like a USB C port which will future proof it.
Personally, I'd try and stretch to the Dell if that budget is possible.
There's a whole range of options out there so it's useful to narrow it down a bit.
Budget is obviously the main thing, how much do you want to spend, new or second hand?
The size/weight, will she be carrying it around all day or is that not too important? Will it get bashed around or will it mainly be sat on a desk? Will it be used standalone or mainly with a keyboard and monitor?
How important is battery life?
Is it Word or is it just some form of word processor (e.g. would google docs be OK)? Is it used for anything else, gaming, programming, etc