Chancellor George Osborne tweeted that today was " a moving, almost overwhelming day".
Osborne was earlier seen wiping away a tear during an anecdote told by the Bishop of London at Margaret Thatcher's funeral.
Former chief policy adviser to Margaret Thatcher, John Redwood, described her as "the best boss I ever had".
"We had to work very long hours to keep up with her," he said.
Fighting back tears he said:
Asked about protests, he simply said: "It is a free country."
The carriage made its way at a pace of 70 steps per minute down The Strand, Temple Bar, Fleet Street and Ludgate Hill to St Paul's. The wheels of the 1.5-ton carriage had been changed from steel to rubber so it runs more quietly on the road.
The Band of Her Majesty's Royal Marines Portsmouth led the procession, striking eight bass drum beats to set the pace and playing funeral marches by Beethoven, Mendelssohn and Chopin.
The route was lined by members of all three services in full ceremonial day dress, officers wearing black armbands, with colours draped and rifle muzzles pointed downwards towards the ground as a mark of respect.
More than 4,000 police officers were on duty to ensure security amid heightened fears of a terror attack sparked by the bombing of the Boston marathon in the US.
As the procession moved forward, a gun salute was fired at one-minute intervals. Among the three 105mm light guns operated by the Honourable Artillery Company were two used in the Falklands, which were last fired in anger at Goose Green and the final assault on Port Stanley.
Boris Johnson said the crowds that had turned out to pay their respects to Baroness Thatcher were "an astonishing comment on her power".
He told ITV News: "I think it's an astonishing comment on her power, the way she spoke to people, after all the controversy over whether this was the right way to commemorate her today, the right kind of funeral to have, look at the size of the crowds who have turned out to pay their respects."
An admirer of Margaret Thatcher, who is in Whitehall to watch the funeral procession, has had a tattoo imprinted on his leg in memory of the Iron Lady. Dave had the body art done yesterday and said: "There's no such thing as an archetypal Thatcher fan."