Here is the current Archers sig-tune, a movement entitled ‘Barwick Green’ from a Suite by Arthur Wood, in the recording that was used between 1951 (the very first episode) until 1992, by Sidney Torch and his Orchestra:

Sir Harrison Birtwistle’s Deep Time (2016): the UK premiere given during BBC Proms 2017 by Staatskapelle Berlin conducted by Daniel Barenboim: