An additional £2bn for councils to provide adult social care over the next three years was announced by chancellor Philip Hammond in his budget on Wednesday (8 March).
Lord Porter, chairman of the Local Government Association, said adult social care faced significant pressures and the additional money was desperately needed.
The Rural Services Network has also campaigned for extra social care funding.
Lord Porter said: "We are pleased that the government has started to act on our call and found a way to help councils plug some of the social care funding gaps they face."
The extra £2bn for adult social care marked a significant step towards protecting the services caring for the most vulnerable in local communities, said Lord Porter.
"Councils must have full flexibility over how they use this funding to ensure it helps people live independently in their communities and surrounded by their families and friends."
It was also important that authorities were able to provide support to older people and those with mental health conditions, learning and physical disabilities.
"Adult social care is vital in its own right, as well as easing the pressure on the NHS," said Lord Porter.
"Councils want to give people the best possible chance of staying out of hospital and to get them home quickly if a hospital stay is necessary."
But Lord Porter said the additional money was unlikely to resolve the situation.
Local government faced a overall funding gap of £5.8bn by 2020 and all councils would need to make continued cutbacks to local services, including social care, over the next few years.
Lord Porter warned: "Short-term pressures remain and the challenge of finding a long-term solution to the social care crisis is far from over."
The government had commited to publishing a Green Paper to explore options for a long-term solution is recognition of this, he added.
It was important that the issue did not not end up being kicked into the long grass like other social care reviews, inquiries, commissions and their recommendations over the past decade.
"With councils facing further funding pressures and growing demand for support by the end of the decade, this is the last chance we have to get this right.
"For that to happen, local government leaders must play a fundamental part. All options must be on the table and it needs cross-party national support."