The future of the Duke of Edinburgh title
Currently the heir to the Edinburgh title is Prince Charles as the eldest son of the title-holder.
The Letters Patent provision of 'heirs male of the body' means that Charles will inherit the Edinburgh title on the death of his father.
• If that happens while the Queen is still alive then Charles will add the Edinburgh titles to his present titles. When Charles becomes King the Edinburgh title will merge with the crown.
• If Philip outlives the Queen then the Edinburgh title will pass to Charles, who is already King, and thus will automatically merge with the crown.
It is then intended to recreate the Edinburgh title for Edward.
• If Charles predeceases the Queen then the title would pass to William, who presumably would honour his grandmother's stated wish but...
• If Charles and William predecease the Queen then that sitution reaches Harry, who again presumably would honour his grandmother's stated wish but...
There is a scenario whereby the title is not available for anyone to regrant it to Edward:
• William marries and has a daughter (or a couple of daughters) but no son.
• Charles, William and Philip die before the Queen leaving the daughter (or eldest daughter) as the Queen's heir - then Harry inherits directly the Edinburgh title and it doesn't merge with the crown.
The current succession to the Edinburgh title is the same as for the throne in the first four people.
Harry inherits and it merges with the crown
add a daughter in there for William and it changes:
William dies leaving the daughter as heiress apparent (can't be replaced by a son)
Harry becomes Duke of Edinburgh and Edward misses out.
The deaths above can happen in any order so long as the three men die before the Queen and William has a legitimate daughter and no sons.
Of course Edward could also inherit the Edinburgh title directly from his father - if:
• Charles, William, Harry and Andrew all predecease Philip (or again William and/or Harry leave only legitimate daughters) then the title would pass to Edward by direct inheritance (along with the Merioneth and Greenwich titles).
Harry can't inherit the title, as it is currently set up, from Edward as Edward has a son who would inherit it assuming that a new regrant would use the standard Letters Patent of 'heirs male of the body'. It would be strange to set LPs for a new title that grants the father only the title and not allow it to go to his son when his other titles - Wessex and Severn - will go to James.
There is no way that BP can say that Edward would definitely get the Edinburgh title as they are fully aware of the inheritance possibilities and so know that there is a chance that
a) Edward won't get it at all or
b) that he could get it through direct inheritance or
c) the most likely that he will get it as a regrant when it merges with the crown at Charles' accession.