Fantasist Carl Beech made claims there was a VIP paedophile ring operating in Westminster, which were eventually found to have no basis, and was jailed.
Lord Brittan was falsely accused of sex crimes by Beech and died in 2015 aged 75 before he was publicly cleared.
Lord Watson of Wyre Forest apologised to the former home secretary's widow.
The appointment of the ex-West Bromwich East MP to the upper chamber faced criticism over accusations he "destroyed" lives by championing claims made by Beech, known as "Nick".
A botched police inquiry into the allegations, which cost millions of pounds, saw dawn raids on the Brittans' home, among others.
In the Lords, Lord Watson, 55, apologised to Lady Brittan, the widow of Lord Brittan of Spennithorne, who served in Margaret Thatcher's Conservative government.
He told fellow peers: "The first area where I think consensus is always better than disagreement is police reform.
"I apologise unreservedly to Lady Brittan for the role that I played in the investigation of historic child sexual abuse.
"Her experiences led to several recommendations about how the police conduct themselves.
"I'm sorry and I owe it to her to work to achieve those aims in this House in the months and years ahead."