Police chief in charge of security says officers have power to step in if 'harassment, alarm or distress' is caused

Protesters could be arrested for "alarming or distressing" mourners at the funeral of Lady Thatcher, a police chief in charge of security at the event has warned.

Commander Christine Jones, who oversaw the wedding of Prince William to Kate Middleton, warned that officers had power under the controversial section 5 of the Public Order Act to step in if non-violent action was the cause of "harassment, alarm or distress" as Thatcher's coffin makes its way through London to St Paul's Cathedral.

Nearly 3,000 people have joined the Facebook group "Maggie's Good Riddance Party", which claims it will hold a "right jolly knees up" outside St Paul's on the day of the funeral. A group of Liverpool football fans attending an away match against Reading sang: "Lets all do the conga, Thatcher is a gonna …" A banner in the stadium read: "You didnt care when you lied, we didnt care when you died."

Around 3,000 people gathered in a rainy Trafalgar Square on Saturday night to "celebrate" Thatcher's death. The protest passed off relatively trouble-free with five arrests made by the 1,700 police present.

Scotland Yard has already asked protesters planning to turn their backs on the coffin as the funeral carriage passes to let them know in advance. However, Shami Chakrabarti, the director of Liberty, said she was concerned that the police should focus on public order and not make judgment calls about manners.

She said: "Some will question the taste of funeral protests, whilst others will see them as inevitable at such a public political event. Either way, the authorities have no role in policing manners, and it would be tasteless indeed if the memorial of any democratic leader prompted arrests of peaceful protesters and the strangling of dissent."

Carol Thatcher, the former prime minister's only daughter, broke her silence on her mother's death. Wearing a black shawl, black trousers and clutching a pair of sunglasses, the former journalist posed for photographers with her brother, Sir Mark, after giving a statement outside the family's house in Chester Square. She said: "I would just like to say that I feel like anyone else who has just lost a second parent. It's a deeply sad and rather thought-provoking moment in life. My mother once said to me, 'Carol, I think my place in history is assured.' The magnificent tributes this week, the wonderful words of President Obama, and others of colleagues who once worked alongside her, have proved her right."

Thatcher thanked those who had sent her "messages of sympathy and support", adding: "These have given me strength. But I know this is going to be a tough and tearful week, even for the daughter of the Iron Lady."

The scale of the involvement of the military in the funeral, which will start at 11am on Wednesday, also became clear. Three military bands will play along the route, followed by the funeral cortege, while serving miliary personnel will greet the coffin on the steps of the cathedral. Two serving survivors of the Sir Galahad, sunk during the Falklands conflict in 1982, are in the escort party, brothers Sgt-Major Bill Mott and Welsh Guard Major Nicholas Mott. A 19-gun salute will be fired from the Tower of London during each minute of the procession from St Clement Danes to St Paul's, the route of which will be lined with more than 700 military personnel.

The military's involvement in the funeral has reportedly caused concern in Buckingham Palace. One senior Labour figure told the Observer that he believed the "militarisation" of the event was inappropriate and that the £10m expense was too high at a time of austerity.

Other details in the order of service have been released by Downing Street. The west steps of the cathedral will be lined by 14 Pensioners of the Royal Hospital Chelsea.

Thatcher's son, Mark, a controversial figure who was convicted in 2004 of involvement in an attempted miliary coup in Equatorial Guinea, will not play a major role in the event. However, his children, Michael and Amanda, will carry cushions bearing the Insignia of the Order of the Garter and the Order of Merit and lay them on the Dome Altar. Amanda will read from the King James Bible.

• This article was amended on 14 April 2013. The original version stated that a 19-gun salute would be fired during the funeral from London Bridge, instead of the Tower of London.