A quick look at the CBP's FY 2020 budget shows that it's main source of income is the Congressional appropriation of $445 Million.
Keep in mind that CPB's sole purpose for existence is to be a buffer between Congress and the stations. That's how it's explained in the Act. The BBC, on the other hand, is a full-fledged TV and radio network, creating programming, and operating stations. Two very different kinds of operations.