The move comes after the organisation ran out of money and lost hope of securing more funds from the Construction Industry Training Board.
Donations from construction companies raised £400,000 for the charity to keep it going in the short-term last year.
Steve Radley, Director of Policy at CITB, said: “We have given a clear outline of our funding criteria, which we agreed with industry through extensive consultation last year.
“Crucially, all applications must be employer-led. Funding will be given only if other sources of funding are not available.
“Applicants must also provide solid evidence of how their project will benefit industry.”
Building Lives said: “Given the skills crisis in London, it is incredibly disappointing that we are unable to continue with our model, especially as it provides huge value for money for the tax payer.”
The orgaisation’s 16 staff are being made redundant while “training academies will be handed back to Building Lives’ partners to determine their future purpose from 30 June 2016.”
Building Lives was started by Lakehouse founder Steve Rawlings in 2010.
Building Lives Managing Director Sian Workman said: “In order to continue operating for another year, Building Lives needed £900,000 to deliver 380 Careerships across four Training Academies based in the heart of London Council Estates.
“That’s a drop in the ocean compared to how much money is spent for no guaranteed job outcomes.
“The bottom line is, although a Careership may not have fitted with existing government funding criteria, it led to real construction jobs, helping reduce unemployment and the skills shortage – ultimately, benefiting us all.
“I am deeply disappointed we have failed in our attempts to secure the financial support needed from government and the construction sector to continue. However, I am also incredibly proud of what the team has accomplished since Building Lives first opened its doors.
“Proud that we dared to be different and in the process supported more than a thousand people into construction careers.”