BBC Live Subtitles are available on all channels apart from BBC Parliament, BBC Alba and S4C.
https://www.bbc.co.uk/iplayer/help/using_subtitles
Most of the programmes on BBC iPlayer now have the option to turn subtitles on. I think a very rare, old, program that does not have it. As the standards state MUST http://www.bbc.co.uk/accessibility/guides/subtitles/
The standards are clear. 4.1. Full-length scheduled programmes and their associated broadcast subtitles MUST be made available online through iPlayer.
http://www.bbc.co.uk/guidelines/futuremedia/accessibility/su...