Paul denied he was the father...but Anita was paid pounds 5,000 to keep quiet; `Why not suggest to Paul he be man enough to write to me?'.
It gave young mum Anita Cochrane a payment of pounds 5,000 - provided she agreed to keep quiet about her claims that Paul was the father of her son Philip.
The secret document was reluctantly signed more than 30 years ago by Anita after being drawn up by the Beatles' solicitors on behalf of the late Brian Epstein, their manager.
It was an attempt by Epstein to prevent bad publicity at a time when the clean-cut group were about to conquer America - Can't Buy Me Love had just become their fourth British No 1.
The gagging order worked - Anita has still never revealed her astonishing claim about the father of her son, who is now a 33-year-old lighting technician living in North London.
But The People has a copy of the agreement, dated April 23, 1964, which was also signed by 17-year-old Anita's mum Violet and Bob Houghton, who was living with Violet at the time.
The agreement barred them from going public or going to court.
It meant she could not speak to anyone about her claim that Paul - back at No 1 in the charts with his new album Flaming Pie - was the father and couldn't even talk about the fact that the all-powerful Beatles team had gagged her.
Infringing the order would mean the pounds 5,000 would have to be repaid by the hard-up young single mum.Bob, now 72, said: "We were conned from start to finish.
"When Anita's solicitor Dennis Green read out the contents of the agreement in his pokey office she started to cry.
"The part that upset her most was the fact that McCartney refused to admit he was the father.
"Green assured her this was a legal formality and that the pounds 5,000 was ample proof McCartney was the father.
"We all signed the agreement - myself very reluctantly. I thought the money was a poor substitute for little Philip Paul not to be able to say who his famous dad was."
Anita signed the agreement two months after Philip was born at Billinge Hospital, near Wigan, Lancashire, on February 10, 1964. But before she caved in to the Beatles management machinery, she wrote a letter begging for recognition.
She didn't want money, just status for her child.
The emotional letter was delivered to McCartney's widowed father James at his Wirral home across the Mersey from swinging Liverpool.
It implored Paul to be "man enough to write to me himself".
It said: "I feel sure that you and your son are also aware that I entered into, jointly with my mother, an agreement, in the form of a secret deed with NEMS Enterprises whereby I was paid the sum of pounds 5,000 in consideration of my keeping silent about the affair.
"Whether or not this money, or any part of it came directly from your son Paul I do not know.
"What I do know is that in the aforesaid deed your son has seen fit to deny that he is the father of my son Philip Paul.
"I might add at this point, that my son, at six months old, is the image of his father.
"I take the opportunity of adding also that no-one else could possibly be the father..."
The letter added: "From when the time comes that my son is able to understand, and for as long as I live, Philip will be told who his father is.
"Since my family and I entered into, and signed "the document of lies," on reflection, we regret the act."
The letter ended: "I await a reply from one source or another. Why not suggest to Paul that he be man enough to write to me himself."
Bob said: "Anita and her friends were Beatles mad and regulars at The Cavern Club. After concerts she and her pals and the lads in the band often went back to John Lennon's house in Gambia Terrace.
"When Anita got pregnant she confessed that Paul McCartney was the father so that's when I went to see a solicitor.
"Sadly we didn't make any progress and after several weeks he told us the only thing was to apply for a maintenance order at the magistrates' court."
By March the young mum had a court date for her paternity claim but the night before the Beatles solicitors made a cash offer to Anita.
"They were prepared to pay Anita pounds 2 10s (pounds 2.50) a week for an indefinite period, and all other expenses relating to the birth and her legal costs," said Bob.
"We weren't prepared to accept it and for the next five days she stayed at home nursing the baby.
"She had a call from Brian Epstein to the effect that McCartney would not admit to being the father now he was famous but was prepared to accept "unofficial" responsibility.
"That was when their management team offered Anita a one-off payment .
Bob launched a campaign to gain recognition for Philip Paul and was even arrested for leafleting Liverpool with details of the claim. Before the settlement, Bob wrote a poem on behalf of little Philip, part of which reads:
"My mum she tells me stories,
"They're all about my Dad. I see him almost every day, he always seems so glad. He knows of our existence, he sings of Yesterday', His troubles seem so far away, now that is what I say..."
Philip has said: "I've have incredible offers of money to talk about Paul but it wouldn't be right.
"I don't want anything from him but I've often wondered if he knows that I really do exist." Philip could not get a job when he left school and survived on unemployment benefit.
His true identity was an open secret in the Crosby area of Liverpool.
One close friend said: "It was common knowledge in Liverpool that Paul McCartney was Phil's dad. Everyone knew but people didn't rib him about it .
"It would even be embarrassing having McCartney pictures on the wall or having a Beatles track playing when he came over."
Sir Paul's publicist Geoff Baker said last night: "It's an old story from years ago. There was not a word of truth in it then and there isn't a word of truth in it now.
"Lots of people have made this sort of accusation and they've all been wrong."
WHEN IT WAS '64!
In 1964, the average weekly wage was pounds 16 4s 11d (pounds 16.25) - so pounds 5,000 would have been a fortune.
Going to Anfield to watch Liverpool cost 20p for a place on the Kop or 75p to sit in the stand.
Five grand would have bought TEN Ford Anglias. Or you could have bought a smart new semi in a decent area, carpeted and furnished it, then gone off on holiday - and still had pounds 500 left.
It was in 1964 that the Beatles sky-rocketed to super-stardom.
A string of No 1 hits around the world included I Want To Hold Your Hand, Can't Buy Me Love, A Hard Day's Night, and I Feel Fine. They also had their first triumphant tour of America.
NOW THIS DEED WITNESS as follows:-
1. IN consideration of the payment of
FIVE THOUSAND POUNDS by Nems to Miss Cochrane
by the direction of Mrs. Pillans the receipt and
payment whereof Miss Cochrane and Mrs. Pillans hereby
respectively acknowledge Miss Cochrane and Mrs. Pillans
hereby jointly and severally covenant with Nems as
(1) Not at any time or in any circumstances
whatsoever to make or to cause to be made
any complaint or application to any Court
by way of affiliation proceedings in respect
of the said child against Paul McCartney.
(2) Not to make any allegation or statement
to any person under any circumstances that
or to the effect that Paul McCartney is
the father of the said child.
(3) Not to disclose to any person in any
circumstances the existence of or terms
of this agreement.