McCartney and Asher often went on holiday together, when their busy schedules allowed. In September 1963 they spent two weeks in Greece, where The Beatles were still relatively unknown, with Ringo Starr and his future wife Maureen. Later on the pair tended to have weekend breaks in the countryside, to escape from the mayhem of life in the public eye.
I think we expected Paul and Jane Asher to get married. They were lovers, they were together, and it seemed a natural thing to do. I don't know in the end what actually broke them up. We'll have to ask him about that, or ask her - that's probably more interesting!
Another holiday, again with Ringo and Maureen, was spent yachting in the Bahamas. There McCartney wrote Things We Said Today about his relationship with Asher. He also wrote And I Love Her, You Won't See Me, We Can Work It Out and Here, There And Everywhere about her.
Despite the heady days of life in London and beyond, Asher's main passion was for acting. She was independent-minded and wanted to have a profession in her own right, rather than merely be a Beatle's partner. She was opinionated and refused to sacrifice her career for McCartney, which caused some friction in their relationship.
My whole existence for so long centred round a bachelor life. I didn't treat women as most people do. I've always had a lot around, even when I've had a steady girl. My life generally has always been very lax, and not normal.
I knew I was selfish. it caused a few rows. Jane left me once and went off to Bristol to act. I said OK then, leave, I'll find someone else. It was shattering to be without her.
The Beatles, Hunter Davies
Asher helped him find the house in Cavendish Avenue, London, which they moved into in 1966. It has been claimed that while spring cleaning one day, she inadvertently threw away a notebook containing the handwritten lyrics to a number of early Lennon-McCartney songs.
Also in 1966 she persuaded McCartney to buy High Farm in Machrihanish, Campbeltown, Scotland, suggesting that they should have a place to retreat from the public eye.
We had a good relationship. Even with touring there were enough occasions to keep a reasonable relationship going. To tell the truth, the women at that time got sidelined. Now it would be seen as very chauvinist of us. Then it was like: 'We are four miners who go down the pit. You don't need women down the pit, do you? We don't have women down the pit.'
In 1967 she embarked on a five-month tour of America with the Bristol Old Vic, appearing in Romeo And Juliet in Boston, Washington and Philadelphia. McCartney flew over to America to celebrate her 21st birthday; during the trip he is said to have had the idea for Magical Mystery Tour.
When I came back after five months, Paul had changed so much. He was on LSD, which I hadn't shared. I was jealous of all the spiritual experiences he'd had with John. There were fifteen people dropping in all day long. The house had changed and was full of stuff I didn't know about.
The Beatles, Hunter Davies
Still an unreconstructed chauvinist in the mid 1960s, McCartney continued womanizing throughout his relationship with Asher. His attitude was that it was allowed since they were unmarried.
He had a relationship with actress Jill Haworth during The Beatles' February 1964 visit to America, which he took care to keep from reaching the press. He also had an affair the same year with Peggy Lipton, another American actress, and scores of groupies across the world.
The press, meanwhile, carried frequent predictions and rumours of McCartney and Asher getting married. Despite the problems in their relationship, they were engaged on Christmas Day 1967. Shortly afterwards, in February and March 1968, she accompanied The Beatles to India.
Their five-year relationship came to an abrupt end shortly afterwards. Jane returned unannounced to Cavendish Avenue from Bristol. There she discovered Paul McCartney in bed with Francie Schwartz, an American girlfriend and employee at Apple.
Jane walked out and sent her mother Margaret to Cavendish Avenue to collect her belongings. Although she and McCartney subsequently tried to mend their relationship, by July 1968 it was over. She announced that their engagement was over on the 20 July edition of the BBC television show Dee Time.
I haven't broken it off, but it is broken off, finished. I know it sounds corny, but we still see each other and love each other, but it hasn't worked out. Perhaps we'll be childhood sweethearts and meet again and get married when we're about 70.
Since their split, Jane Asher has since consistently refused to publicly discuss her time with McCartney, possibly uniquely among members of The Beatles' former inner circle.
Asher met the political cartoonist Gerald Scarfe in 1971 at the 10th anniversary party of Private Eye magazine, of which she is a shareholder. Their first child Katie was born in April 1974; they married in 1981, and had two sons: Alexander in 1981 and Rory in 1984.
Asher's acting career continues successfully today. She has also written three novels and more than a dozen books on lifestyle, cake decoration and costuming, and has developed the best-selling Jane Asher range of cake mixes.
She is the president of Arthritis Care, the National Autistic Society, the Parkinson's Disease Society and the West London Family Service Unit, and vice president of the Child Accident Prevention Trust.
She is also a Distinguished Supporter of the British Humanist Association, and patron of Bowel Cancer UK, the Scoliosis Association and the Leukaemia and Lymphoma Unit at University College London Hospital.
I don't remember the breakup as being traumatic, really. I remember more one time when she was working at the Bristol Old Vic and she'd got a boyfriend in Bristol and was going to leave me for him. That was wildly traumatic, that was 'Uhhhh!' Total rejection! We got back together again but I had already gone through that when we eventually split up. It seemed it had to happen. It felt right.
I liked her a lot and we got on very well. She was a very intelligent and very interesting person, but I just never clicked. One of those indefinable things about love is some people you click with and some people who you should maybe click with you don't. Whatever.
Many Years From Now, Barry Miles