A manifesto published by the youth organisation ahead of next week's general election states that given that the result of the referendum on Britain's future membership of the European Union (EU) will impact young people's futures, they must be "meaningfully engaged" in forthcoming Brexit negotiations.
"We believe that young people are an important stakeholder in decision making," the manifesto states.
"We want the government to do more to recognise this and should ensure that young people are meaningfully engaged in shaping what the UK will look like when we exit the EU."
In June last year, following the referendum vote, chiefs of six leading youth sector organisations including the National Youth Agency, UK Youth and Girlguiding made a similar call for politicians and policymakers to listen to young people's views.
In a joint statement they said: "We are calling on politicians and policymakers to fully and meaningfully engage young people at every level of their discussions over the next few months to ensure their views are heard and acted upon."
And in April more than 50 youth leaders signed an open letter to the UK's main political parties demanding they make firm pledges for young people, as they are "the generation that will live longest with the outcome of Britain's withdrawal from the EU".
However, as yet the government has not announced any formal representation of young people's views in future Brexit negotiations, which are due to begin around 19 June, with the date to be confirmed by EU officials after the 8 June election.
BYC's other manifesto also features five other demands. It calls for the voting age to be lowered to 16, mental health services for young people to be improved, the introduction of a real living wage for everyone, the restoration of funding for youth services, and first aid to be taught in schools.
BYC previously made the same calls ahead of the 2015 general election, but has added the Brexit demand to its 2017 manifesto.
BYC chair Anna Barker said it is important that candidates across the country "listen to the issues that young people are passionate about and tell young people what they plan to do about their priorities".
"I'm really looking forward to hearing back from each political party so we can share their responses with young people," she added.