Each ISP will have their own rules but it's common to find that you can still receive e-mail from your old e-mail address but you can't send through it.
I suggest switching to a new e-mail account (which is not linked to any ISP) well before you change ISPs. That will give you plenty of time to notify people about your new address, while still being able to use the old one, up until you change ISPs.
There are loads of free e-mail services but some of them are best avoided. (e.g. Hotmail and Yahoo Mail both have numerous critics because of frequent server failures and missing mail). GMail is probably the most popular free service but you have to put up with the advertising. (Additionally, some people are unhappy with the fact that all mail is electronically scanned by GMail's system. The purpose is solely to direct relevant advertising to you but privacy campaign groups are still concerned about the potential for misuse).
I love Gawab. It's an excellent free e-mail service which is accessible through a web-based interface or via a client such as Outlook Express. You can register as many times as you like (so you can have an unlimited number of addresses). For details, see paragraph 3, et seq, here:
http://www.theanswerbank.co.uk/Technology/Inte rnet/Question407429.html
Chris