The Refugees (Family Reunion) Bill put forward by Na h-Eileanan an Iar MP Angus MacNeil won cross-party backing from 129 MPs, meaning it will get a second Commons reading and could become law.
If passed, it would allow a wider range of family members to be reunited with refugees already living in the UK, and give them financial support to take claims to court.
Currently, UK Government’s rules prevent refugees in Britain from being reunited with anyone other than their partner or children under 18.
Child refugees who arrive in the UK alone are also unable to bring their parents to join them under the current rules. The restrictions are among the toughest in the EU.
Mr MacNeil said: “Today marks a welcome step forward for many refugees in the UK who are desperate to be reunited with their loved ones.
“It’s fantastic that this new law received the backing of colleagues from across the political divide. It’s clear that this issue isn’t about party politics, it’s about doing the right thing and it was pretty obvious to all of us that families belong together and that children belong with their parents.
“I hope that Ministers come to the same compassionate conclusion: they change their mind and alter the rules – putting an end to the misery of refugee families with the stroke of a pen.”
The campaign has been backed by the Refugee Council, Oxfam, the British Red Cross, the UNHCR and Amnesty International, as well as celebrities including Patrick Stewart, Peter Capaldi, Vivienne Westwood, Anish Kapoor, Alan Cumming, David Morrissey and Neil Gaiman.
Refugee Council chief executive Maurice Wren said: “Today offers a glimmer of hope to refugee families who have been torn apart by war and persecution.
“At the moment, the UK Government’s restrictive rules leave refugees isolated, traumatised and alone in the UK, knowing that the people they love still face untold dangers in other countries.
“It’s vital that MPs stand up for refugee families by supporting this Bill which will enable families to live together, focus on the future and rebuild their lives together in safety.”
Alex Fraser, the head of refugee support at the British Red Cross said: “This is a hugely positive step towards improving the lives of refugees who have been torn apart from their families by conflict and persecution.
“At its heart, the Bill is about keeping loved ones together, but it’s also about providing a safe and legal route to protection that could enable more refugees to rebuild their lives in safety together.”
Amnesty International UK director Kate Allen said: "There are hundreds of child refugees in the UK who have arrived alone. On their arrival in the UK they face a multitude of new struggles - a new language and culture as well as the psychological fallout from incredibly traumatic experiences back in their home country.
"MPs voting in favour of the Bill today is a significant step towards reuniting vulnerable children with their families.”