Virtual networks (where the service provider doesn't operate any transmitters or infrastructure but simply buys capacity from those who do) tend to be cheapest.
Asda Mobile (which uses Vodafone's network) is often cited as one of the best around:
http://www.asdamobile.com/compare_tariffs.html
However their deals are mainly tailored around high data usage. Tesco Mobile (which uses O2's network) might be better for your needs:
http://phone-shop.tesco.com/tesco-mobile/help-and-support/tariffs-payg.aspx
GiffGaff (which seems to have quite a few fans here on AB) also uses the O2 network but, like Asda, tends to base deals around high data usage.
LycaMobile is another firm using O2's network. Even though their 'bundles' generally assume that you want internet access, it might still be worth taking a look at the National Bundle options to see if anything suits you:
http://www.lycamobile.co.uk/en/bundles