More than 700 members of the armed forces drawn from all three services took part in the practice before dawn.
They will line the route of the funeral procession from Westminster to St Paul’s Cathedral on Wednesday.
Margaret Thatcher’s coffin is to be carried in a gun carriage drawn by the King’s Troop Royal Horse Artillery, which was involved in the rehearsal.
Major Andrew Chatburn, the man in charge of choreographing the parade, said the rehearsal “went very well” and it was “vitally important” to stage a trial of Wednesday’s event.
“Timings are most important,” he said.
Maj. Andrew Chatburn, ceremonial staff officer for the Household Division, who was also behind the royal wedding procession two years ago and last year’s Diamond Jubilee parade, added: “Bearing in mind these are sailors, soldiers and airmen who have come in to do this specific task from their routine duties, so it’s new to them.
“They need to see the ground as well so they can get a feel for how it’s going to go and they can perform their duties with confidence on the day.”
The procession band played the funeral marches of Chopin, Beethoven and Mendelssohn as it made its way along the deserted streets for the rehearsal.
The Chelsea Pensioners from Royal Hospital Chelsea did not take part due to the early start, but they will line the west steps of St Paul’s for the real event.
It has emerged that the last portrait of Margaret Thatcher shows her relaxing on a deckchair in the garden of London’s Royal Hospital Chelsea, a retirement and nursing home for ex-British soldiers. Lady Thatcher was a strong supporter of the Chelsea Pensioners.
Scotland Yard’s preparations are ongoing and the force says the security operation on the day will be in line with the perceived threat level.
Margaret Thatcher, who died at the age of 87 on April 8, has been awarded a ceremonial funeral with military honors, one step down from a state funeral.
On Wednesday, Margaret Thatcher’s coffin will initially travel by hearse from the Palace of Westminster to the Church of St Clement Danes – the Central Church of the RAF – on the Strand.
The coffin will then be transferred to the gun carriage and taken in procession to St Paul’s Cathedral.
St Paul’s Cathedral has published a full funeral order of service.
Respect MP George Galloway has said he will try to block plans designed to allow MPs to attend Margaret Thatcher’s funeral.
Ministers want to cancel Prime Minister’s Questions and delay the start of parliamentary business – an approach backed by Labour.
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