Other than The Roku Channel, Roku does not write apps for channels.
If you want channels added to Roku Live TV, TCM will NEVER happen. There is a separate TCM app, but it does require a matching cable/satellite/streaming subscription that includes TCM. Some TCM content is available on Max, but not a live stream.
As for "free" British TV channels, there are tons of them scattered around the various FAST (Free Ad Supported TV) services (LocalNow, PlutoTV, Tubi, Freevee, etc...)
