London (CNN) -- The body of Britain's first woman prime minister, Margaret Thatcher, has been taken to a chapel at Westminster, where it will lie overnight before a ceremonial funeral in London on Wednesday.
A short service for those close to Thatcher will be held Tuesday in the Chapel of St. Mary Undercroft in the Palace of Westminster.
On Wednesday morning, the coffin will be carried by hearse to the Church of St. Clement Danes, the Royal Air Force Chapel, on the Strand.
There, it will be transferred to a horse-drawn gun carriage to be taken to St. Paul's Cathedral, where more than 2,000 guests have been invited for the funeral.
Members of the Army, Royal Navy and Royal Air Force will line the two-mile route. The military held a rehearsal very early Monday morning to ensure that all goes smoothly on the day.
Veterans of the Falklands War will bear Thatcher's coffin into the cathedral.
Thatcher led the country into war in 1982, when British forces repelled an Argentinian invasion of the disputed Falkland Islands, known by Argentina as Las Malvinas.
Before the service, a single half-muffled bell will toll for the arrival of the cortege, according to an order of service released in advance by St. Paul's Cathedral.
Prime Minister David Cameron will give a reading at the funeral, in accordance with the wishes of Thatcher, who planned many elements of the service several years ago.
Margaret Thatcher's granddaughter, Amanda, will also give a reading.
As a mark of respect, the chimes of Big Ben, as the bell and clock tower by the Palace of Westminster are commonly known, will be silenced for the duration of the funeral proceedings, said John Bercow, the speaker of the House of Commons.
"I believe that there can be a profound dignity and deep respect expressed in, and through, silence and I am sure that the House will agree," he told lawmakers Monday.
Roads and Underground stations near the cathedral will be closed and buses diverted as part of a large security operation led by London's Metropolitan Police.
More than 4,000 officers will be on duty for the event, the Metropolitan Police said Tuesday.
The threat of demonstrations by anarchists or anti-Thatcher activists, on top of fears that dissident Irish Republicans may try to act, have heightened security concerns.
Thatcher was the target of a hotel bombing in Brighton by the Irish Republican Army in 1984.
Commander Christine Jones said police had done all they could to mitigate potential risks and threats.
"We wish to deliver our operation in a way that protects public safety within the context of a broader security operation, as with many ceremonial London events," she said.
"The right to conduct peaceful protest is a tenet of our democracy; however, that right is qualified in that protest does not stray into acts of crime or violence or the instigation of crime or violence."
A small number of groups have been in touch about plans to demonstrate as the funeral takes place, Jones said.
"We are working with them, and would ask anyone who plans to protest to come forward and speak with us today," she said.
Thatcher was prime minister for 11 years, from 1979 to 1990. After she was pushed from office after a leadership battle within her own party, she served in the House of Lords as Baroness Thatcher of Kesteven.
A public book of condolences held at London's City Hall will close Tuesday afternoon.