You should look at your ISP website. Tiscali say that you can keep your email address, but I can't say if the others will. If you change ISP, then you will get a new email address. You can also get your new isp to pick up emails from your old one, but you will probably have to use the old dial-up isp periodically to keep the account alive. If your dial-up is on a monthly contract don't forget to change it to pay-as-you go to avoid being billed monthly.
Another hint - Once your broadband connection is active, unplug your dial-up modem from the telephone line, and you will be safe from malicious diallers.