The BBC as a whole, yes - but “BBC Worldwide”: the arm that runs the World Service channel and foreign broadcasting is self-sufficient and does run ads. Though

The BBC as a whole, yes - but “BBC Worldwide”: the arm that runs the World Service channel and foreign broadcasting is self-sufficient and does run ads. Though I’m unsure how the accounting works for profits it gets for programs it licenses out when they’re made by the BBC’s domestically funded divisions.