CNAME alias redirects

[#1]

I have an existing PN homepages website with FQDN of say www.any-name.co.uk (I own any-name.co.uk). I have just  bought a minor variant of the name (say anyname.co.uk) whose DNS is hosted by another ISP. I have amended the latter's DNS to CNAME alias it to the former FQDN e.g.
www.anyname.co.uk. ;  IN CNAME www.any-name.co.uk.
A traceroute shows a search for www.anyname.co.uk is indeed ending up on homepages.plus.net but the web server is then giving a '404 page not found' response.
I am assuming that this is because either:
-  the PN web server's virtual hosting is relying on the client to  resolve the FQDN to an IP address (via the CNAME) which it then sends as a  request to the web server with the actual name in the http header (which is then used to call up the right page) - but the actual name included is www.anyname.co.uk and not the canonical www.any-name.co.uk
or
- www.any-name.co.uk may also, in turn, be CNAMEd by PN - and chains of CNAMESs are not a Good Thing 
Is there any way to make this work pls, short of transferring the domain name to PN and paying a hosting fee - which seems a bit pointless as I don't want any additional PN resources.

[#2]

unless the PN DNS servers know about anyname.co.uk they cannot resolve it.
Hosting domains is free on most accounts - you just arrange for hosting only which leaves the billing where it is.