While I can't talk to accessing BritBox directly through Chromecast Google TV, I can report that it's fully accessible through Amazon Prime Channels. From prior experience I know the price is the same as is the viewing experience. You might want to switch the subscription over (and get another free month of viewing in the process).Well right off the hop it didn't pick up my Britbox app. and I can't find it doing a search of Google Play Store from within the Chromecast. I also note that while the Crave app is there, movie or show suggestions (For you) do not include content from Crave. It is still available from withing the app just not served up for you. A minor inconvenience that I'm sure (hoping) will be fixed with future software upgrades.
I also found this Canadian review in my news feed.