Police officers are monitoring social media, internet forums and BlackBerry messaging networks in the expectation that Margaret Thatcher's funeral procession next Wednesday will be targeted by protesters.

The possibility of demonstrations during the funeral has raised concerns that police may adopt the controversial tactic of making pre-emptive arrests.

Plans appear to be under way for different groups to demonstrate during the funeral, and to hold celebrations around the country on the same day.

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Police concerns have been fuelled by the impromptu street parties which broke out on Monday evening in Leeds, Bristol, Brixton, Liverpool and Glasgow – some of which resulted in arrests after clashes with officers.

Police and security-service planning for Baroness Thatcher's funeral has been under way for three and a half years. Officers will probably be required to line the route from the Houses of Parliament to St Paul's Cathedral to make sure that the cortège is not stopped.

The protests present a logistical headache for the Metropolitan Police, whose officers will have to make sure the procession is not disrupted while respecting the public's right to voice an opinion on one of Britain's most divisive politicians.

A Met spokesman said: "London's police, the MPS, City of London and British Transport Police are working together to deliver a security operation for Baroness Thatcher's funeral. Given the nature of the event, our operation will use of a range of appropriate tactics." The Met's first large-scale challenge is likely to be handling anti-Thatcher protests this Saturday evening in Trafalgar Square – a part of London associated with the moment the former Prime Minister's power began to crumble as poll tax protests turned violent.

The Met has made "pre-emptive" arrests in recent years after gathering intelligence about high-profile demonstrations – most notably before the Royal Wedding in 2011. Scores of people were detained in its run-up.

Some of those arrested took their case to the High Court which ruled that, on the facts of the individual cases, the arrests were lawful. An appeal is set to take place this summer. At the time of the original case one of the arguments police used to justify the arrests was that they aimed to protect minority protesters from angry crowds.

Daniel, a 26-year-old from south London who was at Monday night's Brixton protest and is helping to organise something similar for Saturday evening, told The Independent: "There's never been an event with such a publicity run-up. At Brixton, the samba band and a sound system just turned up. Something similar will happen on Saturday. People will come and there'll be a few portable sound systems there."

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He believed protests would only turn violent if the police tried to stop people voicing their opinion. "It would be unwise of the police to come down hard," he said. "Even a heavy police presence will provoke a reaction."

The legislation that allows for pre-emptive arrests is narrow and human rights lawyers have warned against any pre-funeral sweeps.

Michael Oswald, from Bhatt Murphy solicitors, which represented 15 people who were arrested during the Royal Wedding, said: "There must be a concern that the events that took place in Bristol and Brixton will be used by the police to justify the kind of tactics that were seen in the run-up to and during the Royal Wedding.

"Whatever one thinks about the rights and wrongs of protesting during a funeral, the law protects people's freedom to voice their opinions publicly in a peaceful manner."

Politicians from across the political spectrum urged members of the public who disliked Lady Thatcher or her politics to show restraint. Tony Blair said: "Even if you disagree with someone very strongly – particularly at the moment of their passing – you should show some respect." When asked if he was worried there would be similar celebrations when he dies, he said: "When you decide, you divide. I think she would be pretty philosophical about it and I hope I will be too."

The Tory MP Conor Burns, a regular visitor of Lady Thatcher, said she would have been pleased by the reaction. "Funnily enough the parties that we're seeing, the things in some of these mining communities and those young people opening the champagne in Glasgow – they're a remarkable tribute to her," he said.

"I remember telling her about the TUC Congress selling the Thatcher 'death party packs'. She said the fact that they felt so strongly about her more than 20 years after she left Downing Street was a tribute to the fact she had done something in politics rather than simply been someone."

Martin McGuinness, Northern Ireland's Deputy First Minister, said people should "resist celebrating", adding: "She was not a peacemaker but it is a mistake to allow her death to poison our minds."

Former miners in Easington, Co Durham, will mark the 20 years since their pit closed with a party on the day of her funeral. Alan Cummings, chairman of the Durham Miners' Association, said the timing of the events was "remarkable" and "one of those quirks", adding: "She couldn't be cremated on a better day."

He added: "We are inviting ex-miners and their families to go back over their memories of the strike and what has happened since the closure of the pit. I couldn't stand her. She had a very patronising manner and I could have put my foot through the television whenever I saw her on there.

"We opposed and hated everything she did. She has wrecked thousands and thousands of lives so, no, it's not in poor taste. We can understand why people are happy and rejoicing that she has gone because they remember these communities have never recovered."

Meanwhile, Foreign Secretary William Hague today defended the taxpayer contribution to the funeral and the costs of today's debate in the House of Commons.

He said Britain could "afford" to cover some of the costs of next week's events.

Speaking on BBC One's Breakfast programme, Mr Hague said: "It's right Parliament meets and commemorates such a leader of historic proportions in our country's history.

"She changed the course of our history and there have been many comments over the last few days from all corners of the political spectrum.

"When it comes to money, the rebate she negotiated for this country from the EU has brought us so far £75 billion - which is twice the size of our annual defence budget.

"I think that puts money in perspective... so I think we can afford to contribute to a funeral."

Calls made for Trafalgar Square statue

Calls for a statue of Lady Thatcher to be erected on the empty fourth plinth of Trafalgar Square were criticised by Falklands veteran Simon Weston, who warned it could become a target for protests.

Commander John Muxworthy, a Lt Commander on the SS Canberra during the Falklands War, said there should be a permanent public memorial, and that it should be next to Nelson "to recognise that she was at the heart of the nation".

Ukip leader Nigel Farage and Lord Tebbit also said they were in favour. Mr Weston said a statue would be "fitting" but he warned of the "reaction of the foolhardy".

Emma Bamford