Ms Rayner joined ex-home secretary Jack Straw in his former constituency of Blackburn on Saturday for the official unveiling of the statue of Baroness Castle, who introduced the Equal Pay Act in 1970.
Ms Rayner, who was criticised for calling Prime Minister Boris Johnson and his Cabinet “Tory scum” last month, said: “It’s people like Barbara who inspired me to say what you mean and mean what you say and always be true to the people that elect you.”
She said Baroness Castle, who was Labour MP for Blackburn from 1945 to 1979, provided the foundation for the work she and party leader Sir Keir Starmer had been doing.
Addressing about 100 people gathered for the unveiling in Jubilee Square, Ms Rayner said: “I think it’s absolutely fitting that we’re all here today to support what Barbara did when she was your MP, but an absolute treasure to the whole of our United Kingdom, and gave us the cornerstone of what I call our modern society today after that 1945 Labour victory.
“I’m incredibly proud to be here as a ginger northerner who promises to always be outspoken in Barbara’s legacy.”
Mr Straw, who worked for Baroness Castle as a political adviser before succeeding her as MP, said he owed the veteran politician “almost everything”.
He described her as an “extraordinary figure” and a “real force of nature”.
He added: “Barbara was absolutely determined to make her way in what was then a man’s world.”
The crowd listened to a clip from Baroness Castle, who died in 2002 aged 91, speaking on Radio 4’s Desert Island Discs in 1990.
In the clip, she said: “I never wanted a woman’s job.”
As part of the commemorations, children from One Voice Blackburn held placards and marched around the town to the song Everybody Out from musical Made In Dagenham, based on the sewing machinists’ strike at the Ford factory which Baroness Castle helped to resolve.
Sculptor Sam Holland said she had been working on the statue, which depicts the politician striding forward with a copy of the Equal Pay Act in her arms, on the 50th anniversary of the legislation last year.
She said: “I had a real intense moment of catharsis.
“I know how feisty she was and all her accomplishments, not only locally but throughout her career.
“She was a real high flyer in Government and people are really proud of that and are very proud of having had Barbara as their MP.”
Baroness Castle also introduced the breathalyser test and the seatbelt as transport minister in the 1960s.