Originally Posted by 500N
This gives the main bits.
In a very biased, anti-royal manner.
Here is a link which does claim that :the plods" did indeed "shove their guns in the Prince's face", repeatedly shout for him to lie on his face, and took some time to establish his identity.
Prince Andrew's rage at Palace police: Duke angry at officers who mistook him for intruder | Mail Online
Like most things,
the truth is almost certainly somewhere between "out-of-control gun-brandishing thugs threaten to shoot Prince" and "Royal twit throws tantrum at being asked politely for his name".