update: I’ve resolved my issue.
I was using a Contact Form extension (which integrated Contact Form 7 & BWP Recaptcha, I maybe installed this before this integration was available in BWP Recaptcha?).
When I deactivated this, the BWP Recaptcha tab was visible on the Contact Form Settings tab. When I clicked on this, it rendered and generated the snippet, which when I inserted onto the contact form now works a treat.
If you have the same Contact Form 7 Captcha extension (v 0.1.0) then deactivate and try this out.