Complex sentence: The letters are destroyed unopened whenever a prime minister leaves office, so what action to take is only ever known to previous prime ministers--however, all relevant former prime ministers have supported an "independent nuclear deterrent", as does incumbent David Cameron.
Split into simpler sentences: The letters are destroyed unopened whenever a Prime Minister leaves office, so what action to take is only ever known to previous Prime Ministers. However, all relevant former Prime Ministers have supported an "independent nuclear deterrent", as does incumbent David Cameron.