Mayor of London Boris Johnson said the authorities were prepared for potential violence, after trouble erupted at several impromptu street celebrations earlier in the week.
Any unrest is likely to feed concerns about security at the Iron Lady's funeral in the capital on Wednesday, which will be attended by Queen Elizabeth II, Prime Minister David Cameron and 2,000 guests, including many political and world figures.
Former Republican White House hopeful Newt Gingrich; Tim Berners-Lee, inventor of the world wide web; Canadian Prime Minister Stephen Harper and former Australian premier John Howard were among the latest guests confirmed to attend.
No formal demonstration has been organised for Saturday, but almost 1,500 people have pledged on Facebook to attend a "Thatcher's Dead" party at Trafalgar Square at 6:00pm.
Representatives of the coal miners who battled Thatcher in a year-long strike in 1985 before accepting sweeping pit closures, plan to travel to the capital for the event alongside students and left-wing groups, The Guardian reported.
A spokesman for Scotland Yard said officers had "contacted a number of individuals who have stated they intend to take part in protest on Saturday".
London's mayor said people were entitled to demonstrate but warned police would take a tough line on any violence.
"We live in a democracy where people are entitled to protest, they are entitled to have fun and do what they want," Johnson told LBC radio on Friday when asked about the Trafalgar Square event.
"What they can't do, I think, is use the death of an elderly person to begin riot or affray or that kind of thing.
"So we're getting ready for all that. The police are obviously going to be making sure that if people do break the law they will be properly dealt with."
Thatcher 'left detailed instructions'
Police are mounting a major security operation for Wednesday's funeral, when Thatcher's coffin will be taken through streets lined with members of the armed forces to St Paul's Cathedral.
The ceremony itself will be carried out in line with strict instructions left by the former premier herself, according to the Daily Telegraph newspaper.
She requested that Cameron, as prime minister of the day, read a passage from the Bible but did not want any political eulogy, it said. She also asked that her favourite hymns be sung.
In a reflection of her strong partnership with Ronald Reagan in fighting communism in the Cold War, the guest list includes all the surviving US presidents.
However, several towering politicians from Thatcher's era, including former Soviet leader Mikhail Gorbachev, German ex-chancellor Helmut Kohl and Reagan's widow Nancy, are not attending due to ill health.
The guests will join members of Thatcher's family including her 59-year-old twins, Mark and Carol, who were reunited on Friday evening for the first time since their mother's death.
They were both out of the country when Thatcher died on Monday following a stroke at London's Ritz hotel, aged 87.
Mark, who returned overnight on Tuesday, greeted his sister outside the family's central London townhouse following her arrival back in Britain late on Friday, before escorting her inside.
Thatcher, a Conservative, was Britain's only female prime minister and the longest serving British premier of the 20th century, holding office from 1979 to 1990.
Her death has sparked fierce debate about her legacy in Britain.
Her admirers, who credit her with helping to end the Cold War and reshaping the British economy on a more competitive footing, are campaigning for a public memorial.
But left-wing opponents accuse her of unpicking the fabric of society and putting millions out of work with her radical free-market reforms.
An online campaign by Thatcher's critics has succeeded in pushing the Wizard of Oz song Ding-Dong! The Witch Is Dead to the top of the charts, sparking a political row.
Supporters of Thatcher say the song should be banned from the BBC's weekly radio chart show on Sunday.
The corporation has sought a compromise, saying it would not play the song in full but would broadcast a five-second clip.
BBC director-general Tony Hall said the campaign was "distasteful" but insisted it would be "wrong to ban the song outright as free speech is an important principle".