Protesters against Lady Thatcher's funeral are falling into the trap of being as divisive as they accuse her of being, the dean of St Paul's Cathedral has warned as he appealed for the late prime minister to be treated as a "human being".

As Lord Mandelson criticised the "quasi-state funeral" on the grounds that Thatcher was no Winston Churchill, the Very Rev Dr David Ison said the ceremony was "not a political demonstration", but rather a demonstration of "how we respond in the face of death".

Ison, who will give the bidding at the service, said: "There is a lot of controversy about it, yes. But, if the text of the service, which was planned in conjunction with Thatcher herself and her family, was examined, by and large it anticipates some of the criticisms that people might make.

"So there is no tribute. There is no eulogy, and that was Mrs Thatcher's decision. It's not being triumphalist. It's not a celebration of her life and her achievements.

"It is very much a service of commending her in God's love and mercy, bearing in mind that she, like all of us, is human, and will have fallen short of her own ideals, let alone in the way in which we fall short of other people's ideals."

But the controversy over the ceremonial funeral with military honours, which will involve more than 700 personnel from the three armed services, intensified as Mandelson said he would have advised against the funeral.

"I will pass over tomorrow's quasi-state funeral," the former business secretary said of the ceremony, which was drawn up in 2008, the year he returned to the cabinet. "I would have recommended against it – Mrs T is not Churchill – so it's just as well I wasn't asked."

Supporters of Thatcher spoke out on another front as they criticised the US president, Barack Obama, for sending a low-level US delegation to the funeral.

The US will be represented officially by George Shultz, Ronald Reagan's second secretary of state, and James Baker, who was the late president's treasury secretary. Dick Cheney, the US vice-president under the second President Bush, will attend in a personal capacity.

Liam Fox, the former defence secretary, who has close links to US Republicans, told ITV News: "I think a lot of people in this country will be disappointed and surprised, given the way in which President Obama had praised Margaret Thatcher, that no one from the administration is here. I find that quite sad."

David Cameron hosted a small dinner in No 10 on Tuesday night for funeral guests including Cheney, Baker, Shultz and the Canadian prime minister, Stephen Harper.

Thatcher's body was brought to the Commons on Tuesday to allow MPs, peers and friends to pay their respects. Her coffin, draped in a union flag, was driven to the Palace of Westminster before a service attended by 150 people at the Chapel of St Mary Undercroft where it lay overnight.

A procession of eight horses from the King's Troop Royal Horse Artillery will be led by a horse called Mister Twister, according to Downing Street which announced that more than 2,300 guests will attend the service at St Paul's. All 32 current cabinet ministers, including non-voting members, will attend as will 30 former members of Thatcher's various cabinets.

Security for the funeral has been reviewed following the Boston bombing, though nothing has been passed to British security officials to say the attacks were the work of those inspired by the al-Qaida ideology of terrorism, sources say. The home secretary, Theresa May, was briefed by Sir Jonathan Evans, the head of MI5, and Cressida Dick, head of counter-terrorism at Scotland Yard.

Even before the US bombs, the Met's plan for the Thatcher funeral was so large as to lock down parts of central London. More than 4,000 officers will be on duty, one every few yards of the procession route, with exclusion or sterile zones put in place where the public cannot enter.

Police say a small number of people have contacted them to say they want to protest along the funeral route. Most leftwing and anti-capitalist campaigners say the demonstration at the funeral will be smaller than Saturday night's anti-Thatcher protests.

Hundreds of officers will be kept "kitted up" and ready to rush to flashpoints as part of a major security operation.

But the dean of St Paul's stressed that a fellow human being is being mourned. Ison said: "I hope that everyone who watches the funeral will watch it thinking this is a fellow human being and Mrs Thatcher is actually one of us.

"It seems to me that the protesters are trying to do the things they decry Mrs Thatcher for, which is to divide the world into them and us, and to treat as less than human the person or people on the other side."

Quoting the Roman emperor Marcus Aurelius, he said: "The best revenge is not to be like that. Or, as Jesus said: 'Do to others what you would have done to you.'

"That is the message to everybody. It is the message to the protesters, and also to those who are angry with the protesters."

Ison took up his post in May last year after his predecessor resigned in the wake of the row over Occupy anti-capitalist protesters camped outside the cathedral. In the bidding, he will read: "We recall with great gratitude her leadership of this nation, her courage, her steadfastness and her resolve to accomplish what she believed to be right for the common good."

Asked about his recent remarks that some in Britain had not yet recovered "from the hurt and anger" caused by Thatcher's policies, and that memories of those policies were being revived by the present government, Ison said people needed to differentiate between a government and a person. "You have got to ask the question why after 23 years it is still controversial," he said. "The thing that people find difficult on either side is that there are two sides – those who regard Mrs Thatcher very positively and those who have experienced hurt and anger because of what happened to them and their communities, which they see as somehow her responsibility.

"There is this understandable hurt and anger in response to government policies in the 1980s which is still unresolved in certain communities and we need to be open and honest about it."

Any intelligence linking the Boston bombing to al-Qaida would have direct implications for the United Kingdom and for high-profile events such as Thatcher's funeral and Sunday's London Marathon.

The fact that the UK terrorism threat level remains unchanged and the government's emergency committee Cobra did not meet after the attack on Boston explain public comments by the Met commissioner, Sir Bernard Hogan-Howe, that there is no reason to think London is less safe after the Boston attacks.

On Tuesday evening Scotland Yard confirmed that extra stop-and-search powers under section 60 of the Public Order Act have not been invoked, allowing officers to stop people without having reasonable suspicion they are planning to commit crime. Section 60 was used during the 2011 royal wedding, and any need to use it will be kept under review.

Hogan-Howe said there would be extra searches carried out and more officers would be visible on the streets. "We will increase searching. We will make sure we have got more officers on the street looking after people, making sure they are safe. We have no reason to think they are any less safe than they were before the terrible events in Boston yesterday."

"We are just taking more precautions than we might have done otherwise … We would be professionally irresponsible if we didn't take some reasonable steps."