My webpage receives a "callback" from a payment gateway,
My webpage checks its validity and processes the information.
I'd like to then automatically send some of these variables on to a different website URL, where I have another page which can process those values,
How can I do this ? I suppose it's like sending form data but all automated eg. without needing a user to press submit.
Very simple.
Your CFM page has presumably been posted to, or perhaps passed these variables through the URL scope; you therefore have this information in your hand which you process however you like.
You can therefore use those variables in a CFHTTP request to another page to pass the data over. Take a look at the CFHTTP docs on doing a POST request, everything you need will be in there. Exactly like a user sending a POST request, but without the user 
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