London (CNN) -- As a nation prepared for next week's funeral of Margaret Thatcher, hundreds of demonstrators took to Trafalgar Square on Saturday condemning the political legacy of Britain's "Iron Lady."
Meanwhile, as authorities planned a public funeral with full military honors, her daughter talked of her heartbreak and grief over the loss of her mother, the first woman to have become the country's prime minister.
"This is going to be a difficult and and tearful week, even for the daughter of the 'Iron Lady,'" Carol Thatcher told reporters outside her mother's central London home.
With high-profile guests, the funeral on Wednesday will rival those given to Princess Diana of Wales and the Queen Mother.
Meanwhile, protesters staged anti-Thatcher gatherings in central London and elsewhere despite earlier heavy rains.
At Trafalgar Sqaure in central London, activists and former miners rallied around an effigy of Thatcher, whose orange hair was made out of plastic bags. The effigy was paraded around the square, which in 1990 was the scene of rioting against a hugely unpopular poll tax introduced by Thatcher.
Protesters chanted "Maggie, Maggie, Maggie, dead, dead, dead."
Opposition groups called their event a "party" Saturday to celebrate the death of the conservative leader. The T-shirt on the back of one man said: "We're having a party, Thatcher is dead."
Participants carried a makeshift coffin labeled "Society." That was a reference to Thatcher's controversial remark in 1987 that "there is no such thing as society."
Workers unfurled a "National Union of Mineworkers" banner, evoking memories of the yearlong coal miners' strike during the Thatcher years.
One person held a placard stating in part: "War-Monger Destroyer of British Industry. Architect of Casino-Capitalism."
Others popped champagne.
London's Metropolitan Police said its officers will be monitoring the event but that officers would not get involved as long as it remained peaceful. One minor scuffle occurred when police removed equipment from the square.
The guerrilla theater Saturday served as a reminder that Thatcher's political legacy remains highly divisive, partly because many blame her for creating staggering unemployment as she battled unions and reduced or eliminated many government subsidies to businesses.
Tight security for funeral
More information emerged Saturday about Thatcher's involvement in planning her own funeral.
Her spokeswoman, Gillian Penrose, said she asked for whoever was prime minister at the time of her death to give a reading.
Thatcher also specified that she wanted the hymn "I Vow To Thee, My Country" to be sung, Penrose said.
Police plan to intensify security Wednesday.
More than 2,000 guests have been invited, including UK and foreign dignitaries, British military veterans and prominent artists, journalists and business people.
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, and two of her close colleagues were killed in IRA attacks.
Police were called Monday in London's Brixton neighborhood,as well as in Bristol and Glasgow after people gathered to "celebrate" the news of her death.
Politicians have condemned such behavior, saying it shows a lack of respect to her grieving family and friends.
"I feel like anyone else who has just lost a second parent. It's a deeply sad and rather thought-provoking landmark in life," Carol Thatcher said.
She thanked people for their messages of sympathy and support, as well as the appreciation given for her mother's achievements.
"My mother once said to me, 'Carol, I think my place in history is assured.' The magnificent tributes this week, (from) the wonderful words by President Obama to others from colleagues who once worked alongside her have proved that," she said.
Carol's twin brother, Mark, appeared briefly beside her for photographers.
Margaret Thatcher was leader of the Conservative Party from 1975 to 1990, and served as prime minister for 11 of those years.
CNN's Fred Pleigten and Laura Smith-Spark contributed from London. CNN's Per Nyberg, Laura Perez Maestro also contributed. Smith-Spark and CNN's Michael Martinez in Los Angeles wrote this report.