Sir Samuel Brittan, Lord Brittan's brother, has responded to Tom Watson's apology, telling ITV News: "It's a halfway apology, I suppose"
Tom Watson said he was "sad" DCI Paul Settle felt his letter to the director of public prosecutions was a betrayal.
The deputy Labour leader defended his actions, saying he felt there was a risk some alleged victims were not having their voices heard.
Tom Watson has directly apologised to Lady Brittan for comments he made about her late husband in connection to a rape allegation.
"I'm very sorry for the distress caused," Mr Watson said.
Asking whether he became too involved in investigations into historical child sex abuse, Keith Vaz asked Tom Watson: "You're not Sherlock Holmes, are you?"
Tom Watson, Labour's deputy leader, has admitted his regret at repeating an allegation that Lord Brittan was "close to evil".
An alleged sex abuse survivor described Lord Brittan "as close to evil as any human being could get".
"I do regret using that phrase," Watson told the Home Affairs Committee
"That was not a phrase that I used it was an alleged victim that used that phrase, but that wasn't Jane.
"But I do regret using that emotive language, I shouldn't have done and I'm sincerely sorry for repeating it, it was unnecessary."
Operation Fairbank - the inquiry into historical child sex abuse claims involving prominent figures- received around 400 "bits of allegations and information", Detective Chief Inspector Paul Settle has told MPs.
Just three convictions have been secured, he added.
DCI Settle said "an awful lot of information came from the internet and was nothing more than rumour and innuendo".
Tom Watson's letter to the director of prosecutions did not influence the Metropolitan Police's decision to interview Lord Brittan over a rape allegation, the force's commander has said.
Steve Rodhouse told the Home Affairs Select Committee that the decision was "taken in isolation".
He said the force had "reasonable grounds" to interview Lord Brittan as a rape suspect and that there were "legal grounds" to do so.
Rodhouse took over the investigation into Lord Brittan in July 2014.
Under his leadership, the investigation referred the case file to the CPS asking them to review it amid concerns that otherwise there would be "media criticism and public cynicism".
DCI Paul Settle claims he was moved off an investigation into historical sex abuse "for standing his ground" over the Lord Brittan scandal.
DCI Settle claimed he was undermined and sideline after raising concerns over interventions by Labour's deputy leader Tom Watson.
He was previously the senior investigating officer on Operation Fairbank, the inquiry into historical child sex abuse claims involving prominent figures.
He alleged that he was told "to have nothing to do with the investigation - the whole Operation Fairbank".
Asked what he is doing now, he replied: "Not a great deal."
Tom Watson committed a "betrayal" by sending a letter to the director of public prosecutions asking for allegations against Lord Brittan to be reviewed, DCI Paul Settle has said.
Watson was heavily criticised when it emerged that he had written to Alison Saunders in April 2014 complaining about the way a rape allegation against Brittan was being handled.
The deputy Labour leader sent the letter despite having "not expressed any concerns whatsoever" when DCI Settle informed him that Brittan would not be interviewed.
The detective said he and the politician shared a "very strong relationship" - meeting "three or four times" - right "up until that letter arriving".
Tom Watson's information on child sex abuse cases led to three successful prosecutions, DCI Settle said.