Baroness Thatcher died this morning aged 87 following a stroke, it was announced today.
The former prime minister, who had suffered bouts of illness for many years, was said to have died peacefully.
Her spokesman, Lord Bell, said: "It is with great sadness that Mark and Carol Thatcher announced that their mother, Baroness Thatcher, died peacefully following a stroke this morning.
"A further statement will be made later."
It is understood that Lady Thatcher was consulted about details of the funeral arrangements, and made clear that she did not want her body to lie in state.
The streets between Westminster and St Paul's will be cleared for the procession, the date of which is yet to be decided. It will not be a formal state funeral.
The flag at Downing Street was lowered to half-mast in tribute today, while parties were suspending campaigning for local elections out of respect.
However, the reaction was not all in praise of her contribution.
As the news broke, Respect MP George Galloway made an apparent reference to a 1980s Elvis Costello song, tweeting: "Tramp the dirt down."
The union flag flying above Buckingham Palace, the Queen's official London residence, was lowered to half-mast as a mark of respect.
A Buckingham Palace spokesman said: "It's in line with Government policy advised by the DCMS. Union flags (at Government departments) at half-mast on days of significant deaths."
Other royal residences flying the union flag like Clarence House, the Princes of Wales' London home, also lowered their banners.
Prime Minister David Cameron told the BBC: "Today is a truly sad day for our country. We've lost a great prime minister, a great leader, a great Briton.
"As our first woman prime minister, Margaret Thatcher succeeded against all the odds, and the real thing about Margaret Thatcher is that she didn't just lead our country, she saved our country, and I believe she'll go down as the greatest British peacetime prime minister.
"Today is obviously a day we should most of all think of her family. We've lost someone great in public life but they've lost a much-loved mother and grandmother and we should think of them today.
"Her legacy will be the fact she served her country so well, she saved our country and that she showed immense courage in doing so.
"And people will be learning about what she did and her achievements in decades, probably centuries to come.
"That's her legacy but today we must also think of her family."