'It is thought he was kept in post to prevent a member of the Royal Family (I did hear who, but I have forgotten now) succeeding him because of the rule of seniority in promotion, said member of the Royal family being incompetent. He died of cancer in service.'

It didn't work like that. Promotion was by seniority, but commands (like Commander-in-Chief Mediterranean) were decided by the Admiralty. He was a junior Vice-Admiral commanding in the Mediterranean in spite of there being officers senior to him. He was succeeded by Vice-Admiral Sir Charles Cotton, then Vice-Admiral Sir Edward Pellew, who was recalled from the East Indies command. Cotton didn't last long - he went back to take over the Channel Fleet from Gambier and died soon after. Nelson himself was only ever a Vice-Admiral.

Because promotion beyond the rank of Captain was only by seniority there were quite a few elderly Admirals around who weren't really suitable for sea service. It was possible to retire officers when they reached Flag Rank (appointed as Rear-Admiral without distinction of squadron - coloquially known as a 'Yellow Admiral'). This what happened to the chap who became King William 4th (Sailor Billy) who is the only Royal Family member I can think of to whom Tootler may be alluding, although he wasn't particularily incompetent, but lacked experience.