Do you have some idea of what you're paying per minute to mobiles and landlines ?
I know I might sound like I work for them but if you're mostly making voice calls, then 8p/min is lower than on some of the older contracts (and definitely cheaper than most other PAYG deals I've seen, esp if you don't need 200+ 'free' texts - Asda charges 4p/text, Orange 12p (!))
Have not really investigated using data from the Asda service - for a while I did use WAP access on a Siemens (using Virgin Mobile network) to check for mail - small amounts of data and most 'calls' cost from 2p to 5p.
I think you should spend a half hour in carphone warehouse (and perhaps for a 'balanced' view, go also to phones4u too!) and see what they suggest for getting your mail.
Do you access it via web browser, or do you want to have POP or IMAP access (options one would have using MS Outlook Express) - have such info to hand, perhaps set a temporary password and ask for a demonstration. If they are 'too busy' and let's face it, December is perhaps not the best month, visit each of the individual network shops and see if they are clued up and willing to demonstrate, and ensure you can find a phone at a moderate price that allows you to do what you need.
It may be the case that something on a contract at a tenner a month will allow you e-mail quite OK, but it won't be 'all singing, all dancing' - so won't have wi-fi access (so at home, if you have a wireless router, you would get fast access via that and not be using up 'mobile' access quota).