The phrase "a private function" is correct and usable in written English.
It can be used to refer to an event or gathering that is not open to the public and is intended for a specific group of people.
Example: "The company is hosting a private function for its employees to celebrate the successful completion of the project."
Alternatives: "a closed event" or "an exclusive gathering".
West End musicals are still an unpredictable investment: this year saw the premature closure of Betty Blue Eyes, backed by Cameron Mackintosh, based on Alan Bennett's A Private Function and featuring an animatronic pig with the voice of Kylie Minogue.
He had a recurring role in the TV series Horse in the House (1979), played the butcher in the British comedy film A Private Function (1984) and appeared in the play within the play in Franco Zeffirelli's film of Hamlet (1990).
I suspect he had soft spots for the middle-class TV storylines spun by his friends Frederic Raphael, Brian Clarke and Julian Mitchell, and for the Clive Donner-directed adaptation of Rogue Male (1976) and Alan Bennett's A Private Function (1984).
A Private Function is an example of that.
Roles in Comfort and Joy, A Private Function and The Killing Fields followed.
They just book a room saying it is for a private function.
The Israeli Interior Security Ministry said it had not intervened in tonight's gathering because it was "a private function".
But last night he was fine, what you'd expect an experienced speaker to sound like at a private function.
You see it in Alan Bennett, in the intellectual cut and thrust of The History Boys, and also in the social comedy of A Private Function.
Lee, a volunteer member of the LGBT advocacy group Queer Space, had ordered the cake for a private function in Bangor, County Down, in May 2014.
Speaking of pigs, Babe would not want to hear about the hefty one in A PRIVATE FUNCTION (1984), Malcolm Mowbray's irresistible comedy about British postwar rationing.
