ITV4 does the British Touring Car Championship - you should get this on Freeview.
The rest..... might be a different matter
There's Motors TV and that covers a wide range of Motorsports
http://www.motorstv.com/?country=uk
British Eurosport/Eurosport 2 also does a wide variety of Motorsoprts, and they have a show on a Sunday night called Motorsports Weekend.
BT Sport have got the rights to the Moto GP calendar (Not too sure if the BBC are in on this or not - they have been for the last couple of years)
Premier Sports shows the NASCAR Winston Cup Series live (I think).
Sky Sports covers F1 and they show live Elite League and Premier League Speedway (British Eurosport covers the Speedway GP series).