No, unfortunately it's not that simple. All a CNAME does is tell the world that the IP address of the sub-domain is the same as another domain. So you can use a CNAME to send the sub-domain to the same web server as the main domain, but then you need the web-server configured to then do a redirect on that domain. That may or may not be simple to do, depending on your hosting setup.
You can have 123-Reg do this for you, but you have to "register" the sub-domain at a cost of £10, which is quite frankly ridiculous, since you already own the domain, so adding a sub-domain to it costs them nothing.