Anna Turley, chairwoman of the Labour Party, said the Reform leader had “failed to take any action on his mayoral candidate’s racist comments”.
She also criticised Farage for not apologising to fellow school pupils who accused him of racism when they attended London private school Dulwich College in the 1970s.
Turley said: “Farage needs to finally grow a backbone and apologise to those who have bravely come forward and shared their deeply shocking experiences about his alleged behaviour.
“And then show some leadership on this issue by throwing Chris Parry out of his party.
“The division and decline Farage peddles is not the path Britain needs.
Lammy previously called on Farage to “stamp out this 1950s-style hate” from Reform.
He wrote: “I will never be cowed by racism.
“But I will call it what it is. Nigel Farage, you need to clean up your party and stamp out this 1950s-style hate.”
Parry has been contacted for comment.