On the PAYG front, I'd recommend getting something from Asda (Living) as they have quite a range of low(ish) cost mobiles (10 to 50+ pounds, depending on what one wants).
Asda SIM is available free when you get a 5 quid voucher (so you can get a new number each time you top-up, and see if you get a memorable number, at which time you can ditch the original SIM).
Regarding laptops, and a budget of 350 to 375 pounds, you may find a Lenovo (IBM) fits the bill, or a low-end Toshiba.
If you do visit Asda Living, check whether they have any Compaq laptops on the shelves (I bought a Win 7 15.6" model for 247 in February - gave it to my sister though as her need was greater), and more recently when I saw two models but one was unpriced, I asked at the checkout and the guy went into the store room, bringing out 3, including a Lenovo with 4GB RAM at just under 300 quid - would have bought it on the spot if I had had the cash spare!.
There's a Compaq Presario CQ62-220SA - Celeron 2.2 GHz - 15.6″ - 2 GB Ram - 250 GB HDD listed on Google's shopping search, at prices from around 340 - see this link for one seller or this link for the Google search. Beware of really low prices with no rating as some firms appear to be fly-by-nights which may take the money...
You might check the Acer Aspire on this link or check here for other laptops with XP or Windows 7 and a screen of at least 14" (which should get you a full size keyboard, with luck).
Sorry if I have put forward too many options, and I am going on my preference for screen size over portability as the extra space can make a real difference to using a laptop, in my view, as can a decent keyboard rather than cramped (I plug in a full size USB kbd so I don't worry about different laptop kbd layouts).