Can I get Britbox with the remote I have now?
I don't believe it is available through the X1 system. And it has nothing to do with an X1 remote.
As has been noted by a couple of previous responders, Britbox is not available on X1. I have X1 and recently subscribed to Britbox. I have a Samsung SmartTV and the app was installed on my TV. It works fine but you will only see the app on your TV. You have to use the Smart TV remote because the app is running indepentently of Xfinity.
Al least that is the way it is working on my setup...