Tom Watson has issued a defiant response to the prime minister’s demands that he apologise for putting the police under pressure to reopen a rape investigation into former Conservative home secretary Leon Brittan.

Labour’s deputy leader told parliament on Monday that it was the children who had been victims of abuse who deserved an apology after he was urged earlier in the day to “examine his conscience” by David Cameron.

Watson’s statement follows a sustained pursuit of the deputy leader by the Conservatives since last Tuesday’s Panorama programme, which examined his role in forcing police to investigate multiple claims of sexual abuse.

Lord Brittan died in January without knowing that he had been cleared of suspicion from the allegation he had raped a woman. It has emerged that Watson had earlier written to the director of public prosecutions, Alison Saunders, about an allegation of rape when he learned that the police inquiry was being dropped.

Watson had already apologised on Friday last week for saying that Brittan was “close to evil”. When he was asked to respond to a point of order from Sir Nicholas Soames who said he had “vilely traduced” the former home secretary, the Labour deputy leader told the Commons: “I understand that honourable and right honourable members feel aggrieved that Leon Brittan was interviewed by the police and that they are angry with my use of language. But I’m sure that they would also agree that when anyone is accused of multiple sexual crimes by numerous, completely unrelated sources, the police have a duty to investigate, no matter who it is.”

Addressing Cameron’s comments, he said the survivors of abuse have been ignored and belittled for too long. “Earlier the prime minister said that I should examine my conscience. Well, I think we all need to examine our consciences in this house. We presided over a state of affairs where children have been abused, and then ignored, dismissed and then disdained. If anyone deserves an apology, it’s them,” he said.

In unusually tense scenes, as Watson sat down, some Tory MPs shouted “shame” and “disgrace” across the floor of the House of Commons.

In an interview with Heart radio on Monday morning, Cameron had increased the pressure upon Watson. “It’s clear he [Watson] has got a lot of questions to answer and the House of Commons select committees are quite rightly going to ask him some questions. And so I’m sure that he should answer those questions and examine his conscience about whether he’s said enough so far,” he said.

The Conservative MP Nigel Evans, who was cleared of rape and sexual assault allegations after a high-profile trial last year, said Watson’s refusal to apologise for “hounding Leon Brittan beyond the grave” called into question his judgment as deputy Labour leader.

“If he had an ounce of compassion at all then he would realise the untold damage he has done to the Brittan family. The stress and trauma that he perpetrated to them is really quite difficult to put into words – it’s tantamount to a campaign of terror that he’s waged on this family.”

Evans also questioned the propriety of Saunders for passing Watson’s letter to the detectives investigating Brittan. “There’s no doubt that the police receiving that letter from the director of public prosecutions would view it as a clear indication of where they should go,” he said.

Sir Samuel Brittan, Leon’s brother, said Watson should resign. “I don’t think he knew anything about my brother. I think he was just looking for scandal because he’s not intelligent enough to do his proper job as an opposition MP,” he told ITV News.

The MP for West Bromwich East later refused to issue a personal apology to family members of Brittan. He told Channel 4 news: “We can never again allow victims to have their voices unheard in the criminal justice system. All I can say to you is that there is far more to this case than meets the eye.”

Asked whether he would now speak to Brittan’s family, Watson said: “I’m not entirely certain whether that would be productive.”

The alleged rape victim, known as “Jane”, reported the alleged offence to police in 2012 but officers told her in 2013 they had no plans to either arrest or interview Brittan. It is understood that Jane then asked the news website Exaro to arrange a meeting with Watson so that she could tell him about the police response to her allegations.

Watson then announced that he had written to Saunders demanding a review of the police investigation, suggesting that the police were unwilling to investigate Brittan over the alleged rape because of his status.

Detailed extracts of Watson’s letter were published by Exaro in May last year. Watson, who released the letters himself on Monday, wrote: “I am driven to the unpalatable conclusion that the identity of the alleged perpetrator – [name redacted] – may in some way have influenced treatment of the case. I hope I am wrong.” He added that there had been a “sea change in the climate surrounding rape, historic[al] cases in particular. Why is it that the tide has not reached this case?”

Saunders replied saying that the Met police investigation was “a live one” and would forward Watson’s letter to the police.

Weeks after Watson’s letter, detectives interviewed Brittan, who was dying of cancer, under caution at the central London offices of law firm Mishcon de Reya.

Senior Tories remain angry that it took police so long to clear Brittan. A senior Scotland Yard officer wrote to Brittan’s widow last week to apologise for failing to tell the family before the peer’s death in January that he had been cleared of the rape allegations. The mayor of London, Boris Johnson, is expected to receive a full explanation from the Met police this week.

Cameron’s intervention followed several stories about Watson’s involvement in the claims against Brittan. The Telegraph claimed that a senior detective, CI Paul Settle, former head of the Met paedophile unit, stepped down from the VIP child sex abuse inquiry following a series of interventions by Watson.

The home affairs select committee will consider whether to call Watson at a meeting on Tuesday afternoon.