I'd really hope that 400-500 would more than cope with your needs.
Someone on a recent thread had identified 3 or 4 laptops with 6 GB RAM and all in the 300-350 pound range, with 500 to 750 GB of storage.
Admittedly they were 15-16" screens from memory, where I'd go for 17" or larger if possible (Medion used to do an 18" screen) and with DD being a potential user, then for home use you might consider adding USB or wireless Keyboard and Mouse (*) so the laptop can be further back on a table (others have had catastrophes when a dashing child has caused a laptop to fall off the edge, or had drinks spilt in them, but with mouse and keyboard, you can protect the laptop a bit, and a full keyboard may be more suited if you are doing length reports or need a number pad).
(*) for 20-30 quid in Asda you can get Asda or Logitech wireless bundles
If you want to watch movies, look for one with HDMI output so it can be plugged into a larger TV, perhaps... I've just had a quick look and found is.gd/Medion_480 (479 + 6.99 delivery, inc VAT). Although not as well known, Medion has been around for some 10+ years and is based in Germany, and originally sold via Aldi stores, with English speaking support from Germany. Not sure how they have developed, but worth a look, in my view (and if I had the spare cash, I'd buy that laptop myself!).
By the time you add on MS Office (unless you use the free 'Open Office' or 'Libre Office') you'll have a hole in a higher figure :)