Jacqui Smith today risked escalating the row over the arrest of Tory MP Damian Green when she insisted "no one is above the law".

The home secretary told the Guardian that the police must be allowed to carry out their statutory investigation without "fear or favour".

"It is serious when a senior politician is arrested," she said. "But what I am absolutely clear about is that no one is above the law and the police should carry out their statutory investigation without fear or favour."

Smith's comments are likely to anger opposition parties who have called on the home secretary to apologise over the incident.

Smith repeatedly dodged questions over whether she had known the investigation involved a member of parliament, insisting simply that she "didn't know the specifics of the investigation".

Earlier today Jack Straw, the justice secretary, denied claims that Green's arrest and the police raid on his office in the Commons meant Britain was "a police state".

The justice secretary told BBC Radio 4's Today programme: "We are not in a police state. A police state would be where ministers were directing a police operation."

When Green, the shadow immigration minister, was arrested last week over allegations that he had procured leaked documents from a civil servant, the police were not following orders from ministers, Straw said.

"We have an independent police service. What's important here is that politicians do not interfere with the natural course of an investigation."

Straw also said that he expected parliament to review the procedures that led to the police raiding Green's office in the Commons. Green strongly denies any wrongdoing.

With MPs from all parties still furious about the way the police were allowed to search Green's office last week and take away his computer and details of constituency correspondence, Straw said that he was "pretty certain" that there would be a parliamentary inquiry into the affair when the case was closed.

The justice secretary also backed Smith's decision not to apologise for what happened to Green.

"If any home secretary had offered an apology, there would have then been a huge furore about the fact that the home secretary was prejudging the actions and activities of the police without an investigation," Straw said.

Straw said that if the Tories were unhappy about what had happened, they could complain to the independent police complaints authority.

MPs have complained that the raid on Green's office in the House of Commons was a breach of parliamentary privilege – the principle the MPs are entitled to special protection to enable them to carry out their work as members of the Commons.

Straw said that he accepted that in this case competing constitutional principles were in play – the right of MPs being free to carry out "legitimate business" on behalf of their constituents, the independence of the police to investigate, and the importance of protecting secrecy and confidentiality "where it is necessary" in government.

Michael Martin, the Commons Speaker, will make a statement about the affair to MPs when the new session of parliament begins with the Queen's speech on Wednesday.

Today Denis MacShane, the Labour former minister, said that Martin had to assure MPs that what happened to Green would not happen again.

"The police have made a mistake, I think the Home Office bureaucracy have made a mistake, and I think the Speaker on Wednesday has to say this will not happen again," he told Today.

"The inner sanctum of our parliamentary democracy is the Palace of Westminster and, in the Palace of Westminster, MPs, yes they are protected under privilege when they speak in the House of Commons, but there is a broader constitutional privilege that says they can meet anyone, talk about anything, discuss their political passions, they can hold files, and the police, the agents of the state, do not storm in there and start breaking in or going into offices and taking away confidential files that all our constituents think will be treated confidentially."

He suggested that the situation could not happen if the UK had its own written constitution: "In other countries ... the police would never be allowed into a parliament."

But one of Britain's leading constitutional experts, Vernon Bogdanor, professor of government at the University of Oxford, told the programme: "This does seem to me something of a storm in a teacup.

"The important principle is that MPs, apart from when they are speaking in the chamber and dealing with constituents' correspondence, are as subject to the law as the rest of us.

"If the police decide not to take action against an MP which they would against an ordinary citizen then that would be discriminatory.

"Then people might say: 'Well, we are not living in a police state but a state where people, because they have been elected to parliament, have certain exemptions from the law.' That can't be the case. They are subject to the same laws as the rest of us."