Louis Mountbatten was murdered by the IRA in 1979. He was second cousin once removed from Queen Elizabeth II, so I presume he was in the line of succession to the British monarchy. What place was he when he was killed?
A fellow by the name of William Addams Reitwiesner (died in 2010) was a well-regarded amateur genealogist. If his website is to be believed:
http://www.wargs.com/essays/succession/2011.html
Lord Mountbatten's daughter and heir Patricia was, as of 2011, 647th "in line" to the throne. You could count by hand those people above her "in line" to remove those people born since 1979 to get an estimate of Lord Mountbatten's position at the time.
This list does not attempt to exclude people who may have been, or married, Catholics, or I'm guessing anything else that may have excluded anyone from actually inheriting the crown should it have come to that.
To put that list into perspective, in general terms, it's descent from Queen Victoria.
Victoria had nine children. All the descendants of her four sons come first, of course, and the Queen is first in line of those.
Then the descendants of her eldest daughter, the Empress Victoria of Germany.
Then the descendants of Princess Alice. She had:
one surviving son
and then it was her eldest daughter, Princess Victoria of Hesse and by Rhine.
Victoria and her husband started as Battenbergs but anglicised it to Mountbatten during WWI. They had two sons, the younger of which was Louis Mountbatten.
This Victoria's older daughter (Alice), by the way, married Prince Andrew of Greece and Denmark and had four daughters and one son, Philip.
For various reasons, Philip lived with his maternal relatives - his grandmother Victoria and his uncle for much of his childhood and took the surname Mountbatten when he gave up his royal titles in order to marry the Princess Elizabeth of Great Britain. Louis Mountbatten was far closer to the British monarchy as the consort's uncle than as a claimant to the throne.