Kinfauns: August, 1969.

It's fair to say that all of the Beatles were more accommodating toward the "fannage" than was strictly necessary; indeed, ludicrously so by modern standards, which dictate that every Z-lister (and what a disgusting thing it is to live in an age where such an expression even exists) must, needs must, be accompanied by assorted goons to keep the fevered (and no doubt pished) masses at arm's length. Living The Dream, friends, living the dream.
John, possibly more than the others, was acutely aware of that old Faustian pact vis-a-vis fame/fannage/fetc. On the one hand he resented the daily invasions of his privacy that went along with being "Fab". But on the other, particularly post-"pot"/acid, he had mellowed to the extent of actively inviting "fannage" into his house from time to time, not snarling at them when they were there, and smiling benignly all the while. See the numerous examples on these pages. However, there were times when all of "Beatles" simply couldn't be arsed with it, and understandably so.
In August 1969, John and Yoko were living at Sunny Heights, having finally moved out of Kenwood sometime in the new year. They'd bought Tittenhurst, but were waiting to move in. Still the fannage came; in this case, one Barb Fenick, who joined the throng outside Sunny Heights in early August 1969 hoping for a meeting with the Lennon.
To this end she knocked on the door a couple of times. Cutty long story shorty, John's bearded visage appeared from an upstairs window, and told her to (and I both quote and split the infinitive) "Piss Off".
Undeterred, she headed for Kinfauns. No sooner had she gone for a stroll round the garden than George (looking remarkably, not to mention presciently, like Lemmy) appeared, and told her to, and I fetc., "Piss Off". The above pic captures that very special moment.
It's a simple anecdote, admittedly, but a superlative one; twice in a single day (though I'll bet there are many who managed four in a one-er).