Collo, I'm trying on the Royal Navy bit. What I've come up with is that in 1826, Sir Arthur Wellesley, Duke of Wellington, was Constable of the Tower of London, and he decreed that, "Only gallant, meritorious and deserving Sergeants of Her Majesty's Army will bcome Yeoman Warders at the Tower."
Later qualifications included having served 22 years, be a recipient of the Long Service and Good Conduct medal, (15 years of undetected crime). Royal Marines, and later Royal Air Force W.O's/SNCO's were admitted. I can only think that the Royal Navy was excluded as it's impossible for a Royal Navy bloke to go 15 years without getting into some scrape, so none of them have got the LS & GC!!
Having said that, I have read something on the www that Royal Navy are eligible, but it's an unconfirmed source. I'll trawl the MoD site again.