Like KJN, I'd suggest looking for an alternative email provider.
Both Gmail (as suggested by KJN) and GMX (which I prefer) allow you to access your mail via an email client (such as Outlook Express or Windows Live Mail) as well as via the web. Further, using a third-party email supplier means that you can always keep the same email address no matter how many times you change your ISP.
http://www.gmx.co.uk/
BT is usually rated as one of the better ISPs, alongside Plusnet, but the really good ISPs tend to be pricey. For example, Xilo gets excellent reviews but it's not cheap, while Claranet (which I use) is the choice of many major businesses which rely upon top quality internet provision but, again, it's not cheap. (I've got an ADSL2+ service, which gives me broadband at twice the speed of regular ADSL services, with a low contention ratio and no download limits, for £18.11 per month).
You get what you pay for!
Chris