Forwarding a domain name to WordPress

Is there any way I can host WordPress on one domain but use the URL from another?

I’m trying to move a blog from a Typepad blog (which is mapped to a .org.uk domain) and wonder if I can set up WordPress in a .org domain then when I’ve copied some important posts across from TP to WP then set the DNS record Cname in the org.uk domain to .org.

i.e. WordPress would be hosted on the .org domain but the address would be .org.uk

My initial attempts at this have failed as WordPress locks my users out with

Forbidden
You don’t have permission to access / on this server

Thanks, Tom