Pedantic note: 'BBC News 24' dropped the '24' bit eleven years ago. It's just been 'BBC News' ever since then.
Subtitling on BBC news programmes is done by a professional subtitler 'revoicing' what is said. i.e. he/she repeats what he hears, while simultaneously listening to the next bit of speech. ('Revoicing' eliminates both background noise and accents). He/she also has to control the colour of the words on the screen, so that different colours are used for different people. As he/she does so, a computer's voice recognition program then converts his words to text, which the subtitler also has to keep an eye on in order to check that the correct text is appearing.
So, at any one time, the subtitler is listening to one person speaking, while revoicing what the previous person has said, controlling the text colours on screen and trying to check that the subtitles are appearing correctly. It's probably no surprise that they can only work in 15-minute stints!
https://www.radiotimes.com/news/tv/2018-05-16/how-do-tv-subtitles-work/