Housing And Care 21 works with 150 local authorities to provide care for elderly and disabled people, amounting to 35,000 hours of home care a week.
Its chief executive, Bruce Moore, told BBC Radio 4’s You And Yours programme that it could no longer provide high quality care on the funding it was given by local councils.
They in turn have been squeezed by cuts to central government funding.
The firm now plans to find a buyer for its contracts.
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He said: “The (funding) pressures are that local authorities have been squeezed on social care budgets for a number of years and are paying the lowest rate possible (to care providers).
“It means we can’t provide the staff training, the recruitment, the terms and conditions to get really good quality care workers and that’s what older people require.”
He said the firm pays close to the minimum wage and needs to rely on zero hours contracts, which means “we can’t get the best quality care workers and that compromises quality”.
The firm has always been determined to meet standards set down by the Care Quality Commission (CQC) but could no longer guarantee them, he added.
He said the company’s contracts may be sold to other firms with less “exacting standards”.
Mr Moore said local authorities wanted to provide the best quality services but were struggling to fund them.
He added that he thought other care firms would not be re-tendering for contracts either and would “move out” of the market gradually.