The phrase the lady’s not for turning is used by, or of, a woman who asserts her determination to do what she has decided to do.

This phrase occurred, for example, in the following from the Herald Express (Torquay, Devon, England) of Wednesday 27^th January 1999 [page 19, column 2]:

Lady’s not for turning
ALWAYS stand you ground even if it is moving. And that is what Joyce Cahill did all the way from the Strand in Brixham to Cumber Drive.
The Stagecoach driver would not accept her return ticket. It showed the date and time of purchase but the price piece was missing. She felt his attitude was pedantic. She refused to get off or pay the single fare.

The phrase the lady’s not for turning originated in the speech (written by Ronald Millar 1) that the British Conservative politician Margaret Thatcher (1925-2013), Prime Minister of the United Kingdom from 1979 to 1990, delivered on Friday 10^th October 1980 at the Conservative Party Conference in Brighton, East Sussex, England.

This phrase meant that Margaret Thatcher’s government would not tone down its tough economic policies. This is the relevant passage, from page 12 of this speech—source: Margaret Thatcher Foundation:

If our people feel that they are part of a great nation and they are prepared to will the means to keep it great, a great nation we shall be, and shall remain. So, what can stop us from achieving this? What then stands in our way? The prospect of another winter of discontent? I suppose it might.
But I prefer to believe that certain lessons have been learnt from experience, that we are coming, slowly, painfully, to an autumn of understanding. And I hope that it will be followed by a winter of common sense. If it is not, we shall not be diverted from our course.
To those waiting with bated breath for that favourite media catchphrase, the “U” turn, I have only one thing to say. “You turn if you want to. The lady’s not for turning.”

The following explanations are from an Associated-Press account of the Conservative Party Conference, published in the Los Angeles Times (Los Angeles, California, USA) of Friday 10^th October 1980 [Part I: Late Final; page 2, column 6]:

Her message to the party faithful was that the government would not be deflected from its tough economic policies, despite rising unemployment and bankruptcies.
“You turn if you want to. The lady’s not for turning,” she said, a pun on the Christopher Fry play “The Lady’s Not for Burning 2.”

The phrase the lady’s not for turning gained instant popularity. It was mentioned in British, U.S., Canadian and Australian newspapers from Friday the 10^th to Wednesday the 15^th of October 1980. And a Reuter correspondence from London, published in several Canadian newspapers on Friday 17^th October 1980, contained the following paragraph—as published, for example, in The Advocate (Red Deer, Alberta, Canada) of that day [page 6A, column 2]:

Thatcher told the Conservative party annual conference last week her government is not going to perform a policy turnabout. In a headline-grabbing remark, she declared: “The lady’s not for turning.”

By the end of October 1980, the lady’s not for turning had become an idiom. The earliest occurrences that I have found are as follows, in chronological order:

1-: From The Northern Echo (Darlington, Durham, England) of Thursday 23^rd October 1980 [page 7, column 4]:

The toffee queen is sticking

DAINTY Dinah the Victorian toffee queen has had the last laugh over the long-running saga which began when an antique dealer bought her.
The dealer intended to whisk Dinah, a four-foot Victorian statue, off to a buyer in Italy last month.
But officials from Beamish Museum said Dinah had been offered to the museum in 1975. The Co-op, owners of Horner’s old toffee factory in Chester-le-Street, realised its error and after negotiations the dealer agreed to lend Dinah to the museum. The Co-op then agreed to pay to get Dinah off her perch.
But efforts to remove Dinah failed.
Now the North-Eastern Co-op has repaid the antique dealer, and as another Iron Maiden would say: “This lady’s not for turning.”

2-: From an account of a meeting of Cheshire County Council’s Primary Subcommittee on the closure of Egerton Street School, published in the Chester Observer (Chester, Cheshire, England) of Friday 24^th October 1980 [page 29, column 9]:

Chairman of the Primary Education Subcommittee, Mrs. Diana McConnell, told the meeting that the closure was being considered because it would save the committee £36,000 a year—and they were pledged to cut education bills countywide by £5m by 1984.
Feelings were mixed among the residents after the meeting.
“It was very helpful, but all the way through you got the feeling that Mrs. McConnell’s mind is already made up,” Coun. Russell said.
“The lady’s not for turning,” added another disgruntled resident.

Notes:

1 The author of the speech delivered by Margaret Thatcher on Friday 10^th October 1980 was the British playwright and scriptwriter Ronald Millar (1919-1998)—as mentioned, for example, by Margaret Jones in Thatcher and Foot: chalk and cheese in Commons, published in The Sydney Morning Herald (Sydney, New South Wales, Australia) of Monday 1^st December 1980 [page 7, columns 6 & 7]:

At the Brighton Tory Party conference, she [i.e., Margaret Thatcher] achieved world-wide television coverage and put a new political quip into the language with her ringing cry: “The lady’s not for turning.”
It has now been revealed that behind this rather theatrical line in speech-making stands, in fact, a man of the theatre. One of her major speech-writers is Ronald Millar, the London playwright. He drifted into the role by accident, after a dinner-party quip about the poor quality of Tory speech-making.
He now works frequently as an unpaid writer for Mrs Thatcher, treating her very much as he might a favourite actress. She has reacted well to this, showing a not untheatrical skill in bringing out the high points of her speeches. Once again, though, her delivery is a little too perfect. A stammer or two would be humanising.

2 The Lady’s Not for Burning (1948) is a play by the British poet and playwright Christopher Fry (1907-2005).