David Merritt took to social media to claim Boris Johnson had used his 25-year-old son's death to "make political capital" during the BBC Election Debate with Labour leader Jeremy Corbyn on Friday evening.
Writing on Twitter on Saturday, Mr Merritt said Mr Johnson was taking people for a ride.
He added: "Corbyn spoke the truth last night. Johnson lied and used our son's death to make political capital.
"Wake up Britain, this man is a fraud.
"He's the worst of us, and he's taking you for a ride."
Cambridge University graduates Jack Merritt and Saskia Jones, 23, were attacked by Usman Khan during a prisoner rehabilitation event at Fishmongers' Hall on Friday November 29.
Khan attacked five people, including the graduates, armed with two kitchen knives and wearing a fake suicide vest before he was tackled by members of the public on London Bridge and then shot dead by police at point-blank range.
During the BBC debate, the two party leaders were asked about balancing the needs of security against human rights in the wake of the terror attack.
Mr Corbyn said: "What happened on the streets of London was utterly appalling and I was very moved by what Jack Merritt's father said about what his son was trying to do.
"That he wanted a society where you did address the huge problems where somebody committed awful acts; of course you must imprison them, of course you try and rehabilitate them if you can."
Mr Johnson said: "I have huge sympathy for Mr Merritt and the families of both victims and it was an absolutely terrible thing.
"But I still think it's wrong that someone like Usman Khan, who was sentenced to 21 years or 16 years plus five on licence, should have been out automatically on eight years."
But Mr Merritt said on Twitter that there was no justification for cutting the early release tariff and claimed it was just trying to "look tough".
He added: "There is no justification at all for cutting the early release tariff from a half to a third of sentences for all sentences over four years that carry a maximum life sentence - that's just trying to look tough on the backs of other prisoners' suffering.
"If prisoners have engaged with rehabilitation and turned their lives around, why should they be punished for what Khan did?"
- A GoFundMe page set up by Jack Merritt's friends and supported by his family has raised nearly £12,000 in under 24 hours.