The former Conservative Prime Minister died of a stroke here last Monday aged 87. She will be given a ceremonial funeral with military honours, one step down from a state funeral.
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.
Maj 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.
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"Timings are most important," he said.
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, said, "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".
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 Lady 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. She was a strong supporter of the Chelsea Pensioners.