I am reading English singer Marianne Faithfull's autobiography, Faithfull: An Autobiography (with David Dalton; Little Brown, 1994). She and her husband John Dunbar were friends of Paul.
There is a story floating around that Paul had a romantic relationship with Maggie McGivern, who was, supposedly, a nanny for Faithfull and Dunbar's infant son, Nicholas. Their son was born in November, 1965 and McGivern, according to the story, would have become the Dunbar's first nanny soon after that, because the story talks about Paul and McGivern's relationship turning serious during The Beatles' recording of the Revolver album, six months after Paul and McGivern's first meeting.
Interestingly, Faithfull never mentions McGivern in her memoir. Since there are later photos with McGivern and the Paul replacement, who McGivern did have a relationship with, you wonder whether she pushed back the time of the relationship to give a continuity between Paul and the replacement.