gmail is a strong candidate for non ISP dependent Email providers..
www.gmail.com
or any of the old favourites like hotmail, yahoo etc..
another way to do it would be to register your own domain name e.g
dwlpl.com
and purchase some hosting to enable you to have a personal email account e.g.
[email protected] cost per year could be as little as £20 and is much more personalised than a hotmail/yahoo account