I have NTL broadband but still have EMail addresses on Freeserve/Wannadoo/Orange. I just have to go to the Orange site and retrieve my account every 90 days. I access the email via my broadband with no problem.
I can still get all 3 of my emails (ntl and hotmail addresses) weather I am on broardband or dial up. I do have a pay as you go dialup number from my website provider and can use it anywhere in the uk. I have not tried it out of the uk. Perhaps BT pay as you go may work but I dont know
Any confusion here is due to the fact that we assume that angleronnie is changing ISP; if staying with the same ISP and upgrading the service, it is likely that he/she can keep the current email address.
If staying with the same isp the your email addy remains extant, if changing isp but still want to keep the old addy then the mail can usually be accessed via the previous isp's home page. This is true with Orange at least and I have no reason to suspect other isp's are any different but stand to be corrected.