Lord Mountbatten was a British individual involved in the Partition of India. On 17 August 1947, Mountbatten released the specific details regarding the borders which would separate India and Pakistan.
When Prem accused the British of "carving [his country] up slapdash in six weeks," the Thirteenth Doctor noted she would pass his thoughts on to Mountbatten, should she see him again. (TV: Demons of the Punjab)
At one point, Alice Coltrane claimed to have seen the ghost of Earl Mountbatten at the Boat Show. (TV: Turn Left)
Behind the scenes
In the real world, Louis Mountbatten, 1st Earl Mountbatten of Burma, was the last Viceroy of India during British rule, and the first Governor-General of independent India, heavily involved in the partition.
He was also the great-uncle and mentor of Prince Charles, and second cousin once removed of Elizabeth II.
As historical inspiration
The plot of State of Emergency was heavily inspired by a real life conspiracy theory involving Mountbatten. The theory alleged that, in 1968, Cecil Harmsworth King, the head of the International Publishing Corporation, plotted to overthrow Harold Wilson and install Lord Mountbatten as the interim Prime Minister.
Like the fictional Lord Ballister in State of Emergency, Mountbatten was a relative of the British Royal Family who served with distinction during World War II and was held in a high regard by the British public.