I am trying to cast from my chromebook to my TV but I get a message saying 'not supported by YouView 3585. I am unable to find out what this means.
You cannot cast to the Youview box. If your TV has casting built in or you have a Chromecast dongle plugged in then there should be another option proffered to cast to.
TBH I don't know why my Youview box comes up as an option to cast to from my Windows laptop. It doesn't when casting from my Android tablet.
I tried to cast a chamber concert from YouTube. When I pressed the cast icon on the movie panel a window came up saying Bush 192 1681 127 available YouView 3585 Source not supported.
The astonishing thing is that it did work once !
The DIAL protocol is used to identify devices on the network capable of playing content. The YouView box will appear in that list as it's capable of playing Netflix, however it's down to clients to filter the list down to just devices that support the specific content being shared. Sounds like you're using clients that are only seeing the presence of the device, but then not filtering down to specific app presence. That's unfortunately a fault with the client, not the receiving device.