All you will need to change on the router is to alter the ISP settings (account name and password) from Pipex to your new ISP's. No need to change any wireless settings as these are unique to your set up.
Changing email addresses is another matter altogether, as your old pipex address will die. You will need to set up a new address and to change your email program (e.g.Outlook Express) to pick up new emails and to send emails via the new ISP. This means changing the POP and SMTP names from those you currently use.
You will also need to tell everyone your new email address of course, and don't forget to change existing registered addresses such as the one you have used to get automatic emails for responses to forums like this one.