Look for a Core i3 processor, (possibly i5, but probably won't be in the cheap as chips price bracket), at least 4GB RAM, at least 320GB hard disk and a 15.6in screen. Expect to pay £300-£350 and look for Toshiba, Lenovo or HP (maybe Samsung?).
Argos Outlet on Ebay has a refurbished Toshiba for 200+ delivery (under a fiver).
OK, the webcam isn't high quality (but hopefully she won't be posing nude anyway!)
The Toshiba Satellite C660 is a great-quality everyday laptop and features a 15.6 inch TruBrite® display and an elegant white design. Added multimedia functionality includes an Intel HD Graphics card for a rich and vibrant display.
CPU and Memory: Intel Celeron dual core B800. 1.5GHz processor speed. 2GB DDR3 RAM memory. 320GB SATA hard drive.
Display features: 15.6 inch widescreen display. High definition display. Resolution 1366 x 768 pixels. DVD optical drives: DVD+RW/DVD-RW (read/write). Dual layer.
Graphics: Shared graphics. Intel HD Graphics 3000.
Interfaces and connectivity: 2 USB ports. 1 Ethernet port. Wi-Fi enabled.
It'll be an incentive for DD to get a (part-time) job (if any exist) if she decides it's "in for a dig". However, given the majority on Ebay have no warranty and anywhere such as CashConverters / CashGnerator / CEX would perhaps give only a 90 day warranty (and the full set of features might not be tested in that time, so a fault may go unnoticed) it seemed a reasonable choice.
Agree you get (to some extent) what you pay for but 2GB and Celeron dual core should be OK, unless DD wants 50 things running at once
OP can I recommend PhotoFiltre (French author, but there's an English version) which is a FREE photo edit application, and LibreOffice / OpenOffice to be able to get spreadsheed, w.p., and so on, that should be compatible with MS Office if she has to hand in homework as files.