David Winnick, who served as MP for Walsall North for 38 years until last year's General Election, said Labour should have no association with Mosley's money.
The party's deputy leader has faced calls to return more than £500,000 in donations after it emerged the ex-boss of Formula 1, and son of fascist leader Oswald Mosley, had published a racist letter in the 1960s.
Mr Winnick said he believed the money must now be given back to avoid further damage to Labour's reputation.
The leaflet, published as election material for Union Movement candidate Walter Hesketh, said ‘coloured immigrants’ threatened children’s health, bringing tuberculosis, venereal disease and leprosy.
Mr Watson, MP for West Bromwich East, said he would not have given the multi-millionaire the 'time of day' had he known about the racist material but has not said whether he will give the money back. Labour has confirmed it will not accept any more donations from Mosley.
Mr Winnick told the Express & Star: "The half a million pounds Mosley gave should be returned certainly in my view given what has been revealed and Max Mosley being the election agent when the notorious leaflet was issued.
"In my opinion the Labour movement doesn't want any financial relationship whatsoever with Mosley.
"Max Mosley says he has changed his views but what he hasn't done in any way is denounced his father's activities."
Mr Winnick said he believed Mr Watson would have to bow to the pressure and return the money.
He said: "Now this has come to the fore the money should be returned. I think that's the view of most people active in the Labour movement. We want no connection or anything to do with Labour.
"The Tories are the last people to give lectures about financial integrity but the pretty strong feeling is the money is going to be returned. The pressure will come from the Labour movement and the way to deal with it is by giving the money back."
The experienced former politician, who was unseated by Conservative Eddie Hughes last year after almost 40 years as an MP, defended Labour's decision to accept donations from Mosley.
"It is now necessary to show where money comes from and that was a Labour policy," he said.
"We wanted to make sure all donations to political parties were properly revealed.
"In fairness, I'm quite sure it wasn't known at the time about this leaflet."
Mr Watson received three donations from Mosley – £40,000 in August 2015, £200,000 in June 2016 and £300,000 in February last year, part of which was used to back his bid to become Jeremy Corbyn's deputy.
He said in the Commons on Thursday:" If I had thought for one moment that he held the views contained in that leaflet of 57 years ago, I would not have given him the time of day.
"He is, however, a man who, in the face of great family tragedy and overwhelming media intimidation, chose to use his limited resources to support the weak against the strong."
MP Jacob Rees-Mogg, tipped by many as a future Tory leader, weighed in to the criticism of the Black Country MP.
He said: "If I were Tom Watson I would be so ashamed to be associated with someone so hostile to the British constitution and freedom of speech that I would feel obliged to pay the money back with interest."
Simon Hackett, chairman of the West Bromwich East Constituency Labour Party, and head of children's services in Sandwell, refused to comment.