(Posted in 2 parts):
I've helped several people find basic computers and there's one firm which I can thoroughly recommend for a combination of quality, value and excellent customer service. That firm is AC Computer Warehouse. They supply both new and refurbished systems - the products which my friends and colleagues have purchased from them have always been from the refurbished range and these have always been of excellent quality. They're currently offering complete systems from �149 (+carriage):
http://www.accomputerwarehouse.com
Another firm worth taking a look at is Black Barn Computers:
http://www.refurbishedcomputers.me.uk/
I'm sure other people will have their own suggestions, so here's a quick guide to specifications:
Processor speed: 500MHz is adequate for you mother's needs. You might get a slightly quicker response from faster processor speeds up to, say, 1.6GHz. Above this you'd probably notice little difference. (Really fast speeds are only needed for gaming and applications like video editing).
RAM: 128Mb is perfectly adequate. 256 Mb is slightly better. 512Mb is unnecessary for your needs.
Hard Disk: The 6.4Gb drive on the most basic model offered by AC Computer Warehouse would be considered very small by many users but is probably perfectly adequate for what your mother requires. 10Gb should certainly be sufficient.
CD/DVD drives: A basic CD drive is all you'll really need but a DVD drive can be handy for, say, loading free software from magazine disks. CD (or DVD) writers (or re-writers) aren't necessary although they do provide you with the opportunity of creating back-up copies of picture folders, etc.