What ensued was an exchange of letters - effusive even by the standards of Labour's luvvies.
Admitting that he was drunk, Enfield then sent an abject apology to the Minister of the Dome who replied graciously that he thought the comedian was in character.
In a letter to Benjamin Wegg-Prosser, the minister's aide, Enfield said: "There is nothing like a glass of champagne or three on an empty stomach to make a chap happy and boisterous and it was thus fortified that I volunteered to lead a small troop of party-goers in search of the Prime Minister."
But before he could find Tony Blair, the comedian came across the spin doctor and hurled abuse at him. "You're ghastly! Nobody likes you. You should resign," he declared before moving off in search of Mr Blair, who he proceeded to tell to sack his aide.
Mr Mandelson's reply to Enfield's apology was unruffled: "Oi Harry! It's OK. Ghastly is one of the politest things I've been called. I just thought you were in Tory Boy character. You're by no means the first person to call for me to be sacked and I somehow think you won't be the last."
More to the point, will it be Enfield's last invitation to Downing Street.