@richjanz, this answer comes with a disclaimer because I don't have or use the Britbox channel, but I can tell how things work in general.
When you install a channel/app that requires a subscription it will generally ask you to sign in or sign up/subscribe the first time you launch the channel. If you "sign in", you're using the subscription you've established with the provider. If you "sign up/subscribe" you're paying through Roku. Maybe you remember how it went the first time you launched the channel?
If you "sign in", the channel should provide you with a way to sign out. See if you can find that option lurking somewhere in the menu or options. You can try signing out, exiting the channel, and then launching it again to see what happens. You should be able to sign in again just as you did the first time you used the channel.
You would have to cancel your subscription with Britbox, which likely doesn't provide a prorated refund for any unused portion, and then subscribe through Roku. Keep in mind that Britbox will know nothing of your Roku subscription so you will be dealing with Roku if there's any issues.
One important note: Any subscription you pay through Roku will only be available on a Roku device, so if you're using your Britbox subscription via an app on any other platform you should stick with what you have.
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