Gallant was one of those who attempted to subdue the terrorist with a narwhal tusk when he went on a rampage on November 29.
The prisoner was spending his first day on licence at a criminal justice conference since he was jailed for killing Barrie Jackson in 2005 when Khan - who was at the same event - launched the attack.
And Gallant was one of those seen in video footage attempting to stop him.
Karl Turner, Labour MP for Hull East, asked Boris Johnson during Prime Minister’s Questions whether he would “pay tribute to Steven for his bravery that day”?
He said: “My constituent Steven Gallant did a bad thing, for which is serving a life sentence in prison. But on the 29th of November, he was the third man on London Bridge.
“He wrestled the knife-wielding murderous terrorist to the ground so that police marksman could shoot him dead.
“Steven is rightly serving life in prison. But will the Prime Minister congratulate him and pay tribute to Steven for his bravery that day, which no doubt, saved lives?”
Mr Johnson replied: “I think the whole House would agree, I'm lost in admiration for the bravery of Steven Gallant and, indeed, others who went to the the assistance of members of the public on that day and fought a very determined terrorist, and obviously is not for the Government to decide these things, but it is my hope that that gallantry will in due course be recognised in the proper way.”
On Monday, Gallant released a statement through his solicitors identifying himself as one of those on London Bridge that day.
He said: “When I heard the noise from downstairs, I went to investigate. There were orders to stay in the conference hall, but I could tell something was wrong and had to help.
“On my way downstairs I saw injured people. It was obvious who was responsible. Khan was stood in the foyer with two large knives in his hands. He was a clear danger to all, so I didn’t hesitate, I used a narwhal tusk and then a chair to hold him back and prevent him from hurting others.
“Khan also showed us the bomb around his waist in an attempt to frighten us. We then chased him on to London Bridge and restrained him until the police arrived.”
Harrowing footage shows Gallant, wearing a purple top with the sleeves rolled up, and two other men - Darryn Frost, a civil servant, and John Crilly, a former prisoner - running on to the bridge after Khan and tackling him to the ground.
Gallant, 42, and James Gilligan were jailed for carrying out a revenge attack on 33-year-old ex-fireman Mr Jackson.
The pair lay in wait for Mr Jackson outside a pub after believing he attacked Gallant's girlfriend. He is thought to have been bludgeoned with a hammer, kicked and punched to death, according to a 2008 Court of Appeal judgment which dismissed Gallant's application to quash the conviction.
But since going to prison, Gallant, who will be eligible for parole in 2022 subject to approval, has "vowed never to turn to violence again".
Instead he learnt to read and write and is now in his third year of a business studies degree.
He has co-written several plays, one of which was recently performed at the Royal Court Theatre in London, his lawyers at Hudgell Solicitors said.
Gallant said: "Nobody has the right to take another's life and I offer my sincere apologies to my victim's family for the hurt caused.
"I can never bring that life back, and it is right that I was handed a severe penalty for my actions.
"Once I'd accepted my punishment, I decided to seek help.
"When you go to prison, you lose control of your life.
"Your own future relies on the decisions of others.
"Bettering yourself becomes one of the few things you can do while reducing the existing burden on society."
Inspired by the Learning Together project after he met the founders, Gallant applied to take part from behind bars.
As part of the programme he has worked with a team of students in Cambridge producing legal advice guides and has become a mentor.
Losing course co-ordinators Jack Merritt and Saskia Jones, who were killed in the attack, is an "unbearable blow" and the "sense of loss is immense", he said.
Mr Merritt, who Gallant met in 2016, was a "role model and friend", he said, adding: "Jack didn't care who you were, he cared about you and your future, he saw who you could become and did not define you by your past.
"I will miss him badly."
Miss Jones was "highly respected and loved" by those involved with the course, he added.
Gallant has resolved to "keep doing positive things" and was "certain" the pair would wish for the programme to continue.
Although initially reluctant to speak out, Gallant decided to come forward after Ministry of Justice employee Mr Frost revealed how he took on Khan.
Gallant said: "I would like to say a special thanks to Darryn.
"Had he not passed me the narwhal tusk at that crucial moment, not only could I have been killed, the situation could have been even worse."
Gallant described former prisoner Mr Crilly and the chef called Lukasz who also stepped in as "extremely brave", adding: "I would like to say thank you to everyone who did their best on that tragic day and I hope that the injured recover as quickly as possible."