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.
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
Dump out the CGI scope in your CF page, you'll have an element called CGI.HTTP_REFERRER - this is the header which the client's browser *might* send you as additional information, you can pass this around as any other variable.
Bear in mind however it's purely informational; some browsers might not send it at all, others it might be wrong, and some it's just plain spoofed, so don't rely on it.