• See Configuration Options for Sending Messages_specify-the-outgoing-smtp-server-used-to-send-messages-for-an-email-account
• Use Menu: Edit -> Account Settings -> <account name>

Also see Automatic Account Configuration (But it appears you have already set up the second account.)

EddieOGallagher said

I've set up my new e-mail and want to send from it by default rather than the old one.

I clicked 'solved' prematurely. Although I've changed the default e-mail in Account Actions as advised it still come up with the old e-mail when I Send a new message.