The measures are included in a Private Member’s Bill, which has the backing of Strictly Come Dancing champion and EastEnders actress Rose Ayling-Ellis.
The British Sign Language Bill was given an unopposed second reading in the Commons after securing Government support.
Although BSL was recognised as a language in its own right by the Government in 2003, it has no legal protection.
Labour MP Rosie Cooper, who put forward the Bill, said making BSL a legally-recognised language will send a clear message to every deaf person that “their language is equal and should be treated as equal”.
In an emotional speech in the Commons, Ms Cooper recalled her own experiences of growing up as the hearing child of deaf parents.
The MP for West Lancashire said: “Growing up, I saw first-hand the difficulties deaf people face every day. The huge challenges my parents had to overcome, to be heard, to be listened to.
“More importantly, to be understood. Now, I’m told I booked my first family holiday when I was four years old. I don’t remember but I did.”
Explaining the objectives of her Bill, Ms Cooper said: “I want to finally recognise BSL in statute, not just a gesture, but a law which requires positive action from the Government, with real progress putting deaf people on an equal footing with those of us who hear.
“For every deaf person like my parents, who’ve been ignored, misunderstood or even treated as unintelligent for simply relying on BSL, this recognition will be clear and will be a message that their language is equal and should be treated as equal.”
The MP thanked Strictly winner Ms Ayling-Ellis, saying: “Clearly, much of the awareness is due to Rose Ayling-Ellis in Strictly; she proved what my dad always says: ‘Deaf people can do anything, even the impossible,’ such as winning Strictly when you can’t hear the music.
“That 10-second glimpse she gave the hearing world into deafness when the music stopped was truly momentous.
“People became aware and interested in BSL like never before. I know we have much support across the House, so let me say this Bill isn’t about politics. After more than 230 years, this Bill is about doing the right thing.”
Using BSL at the same time, Ms Cooper said: “So, in closing, I’d like to say to the minister, thank you for supporting this Bill. Thank you.”
Conservative former cabinet minister Robert Buckland thanked Labour MP Ms Cooper “from the bottom of my heart” for bringing the suggested change forward.
“Let’s not forget the thousands of people with learning difficulties who use BSL, including members of my family. On her behalf, may I thank her? Thank you from the bottom of my heart,” he said.
Confirming Government support, Work and Pensions minister Chloe Smith insisted the Bill will make a “tangible difference” in deaf people’s every day life.
She said: “This is a national moment because we have seen in popular culture, throughout the autumn, the inspirational success of Rose Ayling-Ellis on Strictly Come Dancing.
“From that we have seen the interest of BSL is on the rise. This Bill is an important next step; we want to seize that moment to help improve the lives of deaf people and those closest to them. It’s a crucial step and it is going to make a tangible difference in deaf people’s everyday life, including by listening to deaf people about how that should be done.”
Speaking before the Bill’s second reading, Ms Ayling-Ellis, 27, told The Big Issue: “If it becomes an official language, which we’ve been fighting for all these years, it will be so emotional for us.
“Because of the massive interest in BSL recently, a lot of people don’t realise how much of a fight the deaf community have had.”
Susan Daniels, chief executive of the National Deaf Children’s Society, welcomed the Bill passing its second reading, noting “this is a historic day for British Sign Language users everywhere”.
She said: “With their language now well on the way to being recognised in law, they can feel jubilant, valued and optimistic about the future.”
David Buxton, chief executive of Action on Disability and former chairman of the British Deaf Association, echoed Ms Daniels, saying this Bill has been “19 years in the making”.
He added: “I now call upon ministers and MPs to do everything they can to get the British Sign Language Bill to royal assent in this parliamentary session.”
The Bill will now undergo further parliamentary scrutiny at a later date.