The trust, which has contracts in three other areas to run Work Programme schemes, blamed a lower number of referrals than projected by the Department for Work & Pensions for the decision, but declined to give numbers for commercial reasons.
The trust said a subcontract to run the back-to-work service was already in place with the Careers Development Group, which it said would ensure a seamless transfer of the scheme.
"Tomorrow’s People regularly reviews all the programmes it is involved with," a spokeswoman for the trust said. "In the case of its contract in Barking and Dagenham, the level of referrals based on initial Department for Work & Pensions projections has not been realised. This lower level of referral has not been sufficient to make the contract a sustainable proposition for the charity in the longer term."
The trust said the Careers Development Group had the economies of scale to support Work Programme customers at the lower rate of referral. It said that its remaining contracts in Bath, Bristol and Plymouth were not under threat.
CDG already runs Work Programme schemes in the London boroughs of Hackney, Stratford and Tower Hamlets. It said the number of referrals to Barking and Dagenham in the first part of the financial year 2012/13 were "a third lower than expected and unlikely to increase", although it also declined to give any numbers.
"This will be a seamless change for Work Programme customers, employers and local stakeholders, and they will enjoy the same excellent service, support and partnership working from CDG as they did from Tomorrow’s People," said Richard Clifton, business development director at CDG.