Can't set up new account in Mail

Mail simply will not allow me to set up a new account. When I plug in the username and password of a perfectly valid email address as instructed, Mail always responds with a message that it is unable to verify account name or password.

There seems to be no setting where I can enter details my web host has given me. The email works perfectly well with Webmail, but Mail is completely useless.

I've tried everything including phoning Apple support, but no one can help.

Any help appreciated.