The coffin is carried on a gun carriage drawn by the King's Troop Royal Artillery
The Queen has led mourners in St Paul's Cathedral at the funeral of Baroness Thatcher, Britain's longest serving prime minister of modern times.
More than 2,000 dignitaries from around the world paid their last respects at the biggest such occasion since the Queen Mother's funeral in 2002.
Lady Thatcher's coffin was carried through streets lined by mourners and members of the three armed forces.
PM David Cameron said it was a "fitting tribute" to a major figure.
Four thousand police officers are on duty in central London, which saw large crowds along the route of her funeral procession, which was conducted with full military honours. There were reports of some protests but not the large demonstrations some had predicted.
The congregation at St Paul's included Lady Thatcher's family and all surviving British prime ministers, Tony Blair, Gordon Brown and Sir John Major, the current cabinet and surviving members of Lady Thatcher's governments.
There were tears, and occasional laughter, as the Bishop of London, The Right Reverend Richard Chartres, paid tribute to Lady Thatcher's forthright character in a simple service, which, at her personal request, did not include any eulogies.
After the storm of a life led in the heat of political controversy, there is a great calm," said The Right Reverend Chartres.
"The storm of conflicting opinions centres on the Mrs Thatcher who became a symbolic figure - even an ism.
"Today the remains of the real Margaret Hilda Thatcher are here at her funeral service.
"Lying here, she is one of us, subject to the common destiny of all human beings."
Chancellor George Osborne appeared to wipe away a tear as the Bishop of London reflected on Lady Thatcher's life.
The day began with Lady Thatcher leaving Parliament for the last time as a hearse took her body from the crypt chapel of St Mary Undercroft in the Palace of Westminster to the start of the military procession at St Clement Danes in The Strand.
The union jack draped-coffin was topped with a large bunch of white flowers and a note, by Lady Thatcher's children Sir Mark and Carol, reading: "Beloved mother, always in our hearts."
A gun carriage drawn by six black horses carried the coffin through the streets to St Paul's, where the funeral service began with readings from the King James Bible by Mr Cameron and Lady Thatcher's 19-year-old granddaughter Amanda, and hymns chosen by the former prime minister.
The service ended with a blessing from the Archbishop of Canterbury, Justin Welby, before the coffin was borne out of the cathedral and returned to a hearse which will take it to the Royal Hospital Chelsea ahead of a private cremation at Mortlake Crematorium in south west London.
Lady Thatcher, who was Conservative Prime Minister from 1979 until 1990, died on 8 April, following a stroke, at the age of 87.
She was accorded a ceremonial funeral with military honours, one step down from a state funeral.
Speaking on BBC Radio 4's Today programme, Mr Cameron said it would have been seen as extraordinary not to commemorate her life.
Asked about those who wanted to challenge his view of Lady Thatcher, the prime minister said: "Of course people have the right to disagree and take a different view.
"But when you're mourning the passing of an 87-year-old woman who was the first woman prime minister, who served for longer in the job than anyone for 150 years I think it's appropriate to show respect."
There were more than 50 guests associated with the Falkland Islands, including veterans from the 1982 conflict with Argentina, but Argentina's ambassador to London, Alicia Castro declined an invitation to attend.
Alan Southern, a former member of the Parachute Regiment who fought in the Falklands War, said: "Lady Thatcher was an absolutely wonderful lady. She loved the armed forces and she did so much for the country, she put the 'great' back in Great Britain."
In total, two current heads of state, 11 serving prime ministers and 17 serving foreign ministers from around the world attended.
Notable absences were former Soviet leader Mikhail Gorbachev, who could not attend due to ill health, and former US first lady Nancy Reagan, who was also unable to come.
Six police forces from outside London sent specialist officers to help with escorting foreign dignitaries.
Various roads along the route were closed from 07:30 BST, and Transport for London has advised drivers to avoid Westminster and the City of London. The roads are expected to be re-opened as soon as possible following the funeral.
There were union jacks on display, as well as flags from the US, Canada, Scotland, Poland and the Falkland Islands.
Wednesday's House of Commons sitting has been delayed until 14:30 BST, meaning the cancellation of Prime Minister's Questions, in order to allow MPs to attend - a move approved in a Commons vote on Tuesday.
The Metropolitan Police said it had been contacted by a small number of protesters to say they were planning action on the funeral route in protest at the impact of some of Lady Thatcher's policies while she was in power.
BBC home affairs correspondent Danny Shaw said although Monday's bomb attack at the Boston Marathon was not believed to have led to any significant changes in security for the funeral, it was expected that the police and public would be more vigilant.
Senior officers acknowledged they had a "difficult" balance to strike between allowing people to express their opinions and maintaining order, he added.
Lady Thatcher's coffin was placed in the Palace of Westminster's Chapel of St Mary Undercroft overnight on Tuesday.
The House of Commons speaker's chaplain kept vigil in the chapel through the night.