In some cases yes.
Unfortunately some ISPs provide email addresses that are not portable precisely to prevent people moving. There are some however, including BT, who do allow email addresses to be retained or rerouted at a small monthly price (around £1.50 per month) and this could be the solution.
Experience of those who do switch email addresses shows that it is actually very straightforward, quick and simple and turns out to be far less fuss than people imagine beforehand. There are a number of email services, gmail for example, that are free, reliable, secure and fully featured.
For a definitive answer – ask your current ISP.
This site has some useful information on this topic.