You could go for a 'free' dialup company - or pay as you go dial up. You only pay for the call charges (at 0845 rate).
Companies like Supanet, also have other tariffs, such as ones where you pay a small amount per month, and you pay a different rate (e.g. 2p/min peak, 1p/min other, etc.). For low use, paying pennies a session will be fine, just get used to the slow speed (Which unless you are browsing pages with higher graphics sizes, you will hardly notice - ebay should be fine unless the page has really big product pictures on it). If you setup your e-mail account on a mail client (Outlook, OE, Thunderbird, Pegasus, etc) Then for e-mailing, you just have to write your e-mails, then connect to send and receive, then disconnect, only being online for a minute or so.
Just remember to disconnect from the internet after every session, or the bill will mount up (You can set your computer to disconnect after x minutes of inactivity).