The quote usually attributed to Churchill is, "Don't talk to me about naval tradition, it's all rum, sodomy and the lash!" The only problem, of course, is that Sir Winston never said it, although according to his assistant, Anthony Montague-Browne, he wished he had. The source of the quote is unknown, but as with many such false attributions, perhaps it's more fun to believe the story than the truth.
As for the traditions mentioned, flogging was officially abolished as a punishment in the Royal Navy on March 29, 1949, though it had not actually been practiced since 1879. On July 31, 1970 the Admiralty Board, citing the requirement for sobriety aboard complex modern warships, ended the daily rum ration for men, which had begun in 1655. So it seems that only one of these grand traditions is left to the sailors of today's Royal Navy. Poor buggers.
The Pogues' album by this name is an absolute classic. No record collection is complete without it.