CNAME & MX record confusion.

[Stroller]

Hi there,

A customer of mine is moving from one hosting provider to another. They have
moved the registrar tag over to the new host, and now DNS.

Initially we want DNS entries to point to the old hosting provider, then
move mail & website services over to the new host.

The new host allows us to edit DNS via a web-interface, so I ran dig to
determine what hosts are in use by the old provider to I can configure
these on the new provider's DNS.

The website is hosted at mydomainname.co.uk NOT www.mydomainname.co.uk

The MX records are:
  $ dig mydomainname.co.uk MX +short
  15 tele.mx.easynet.net.
  5 vavip.mx.uk.easynet.net.
  10 noc.mx.easynet.net.
  $

And I can easily set up MX records on the new hosting provider and these
work.

However, when I add a record to point to the website I get problems. The
website is hosted on the server www.commercial2.easynet.net, so using the
web interface I choose CNAME from the drop-down; mydomainname.co.uk is
already filled out as the origin on the webpage that now comes up and I
fill in www.commercial2.easynet.net as the target.

When I subsequently dig for MX reords I find:
  $ dig mydomainname.co.uk MX +short
  www.commercial2.easynet.net
  15 tele.mx.easynet.net.
  5 vavip.mx.uk.easynet.net.
  10 noc.mx.easynet.net.
  $

This seems to result in mail delivery problems, and I don't understand why.
The CNAME for the website surely shouldn't be treated as an MX, should it?

I'm sorry if this is an FAQ - Google wasn't immediately helpful, this is
driving me bonkers, and obviously I'd like to fix this ASAP. I kinda got a
couple of results on Deja which seemed to be people in a similar situation
to myself, but I didn't understand the explanations.

Thanks in advance for any advice,

Stroller.