I'm guessing that since tourists and subjects of Her Majesty Elizabeth, II stand around for hours watching the Coldstream Guards in their various military ceremonies Michael Powell decided that a story about the guards would be a money maker and tourist bait. I'm sure that The Queen's Guards succeeded on both levels.
It's a pity a better story was not provided in between all the footage of the cream of the British military doing the pageantry they're known for. But it isn't all spit and polish and drill for these guys. They're the best of fighting soldiers for the British army and it's one exclusive club to get into.
The story such as it is has guards officers Daniel Massey and Robert Stephens spending some time away from the guards at Massey's home. Where movie and real life father Raymond Massey hosts them along with wife and mother Ursula Jeans.
The family tragedy that looms large over the household is that of a late older brother who never returned from the desert fighting in World War II. They say he's missing, but Raymond Massey knows better. Later on in some action in some archetypal Middle East Principality where Great Britain has a treaty with the rulers Daniel Massey and Stephens face a similar situation to what led Massey's older brother to be killed.
Quite frankly the plot got in the way of the Coldstream Guards and their ceremonies. And it didn't make a lot of sense. It's a rarely seen film now, but Michael Powell did a whole lot better than The Queen's Guards in his career.