No it is not. Very little is private. You cannot run a private member's club and keep it that way. If you are suspected of allowing such satanic rituals as smoking on the premises, local gauleiters can raid you and shut you down. It does not matter if smoking has the unanimous consent of the members and staff. It does not matter if you are in a club of three. It's a club and rules are rules.
If you run a small Bed and Breakfast establishment you cannot pick and chose who you let under your own roof. Nevermind that you only have two rooms and it is simply a way of paying the gas bill. You cannot turn people away if you don't like the look of them. So that is not private either.
Should you be invited to school to read your poetry or explain how the internal combustion engine works, you'll have to have your records looked into. Similarly if you decide to help out a neighbour by giving their kids a lift to school. A tiny ad hoc, private arrangement must these days fall under the watchful eye of ...Who? Well, anybody, an extraordinarily long list of busybodies.
These days, when you pay for something in a shop, the assistant will say "Can I just have your postal code/telephone number/email/dad's dead dog's name?" If you are foolish enough to have an unsecured WiFi connection, Google will have collected it, along with the picture of your mistress's car that was parked outside the house when the wife was away.
One wonders what the phrase "consenting adults in private" really means these days.