Labour would spend around £17 billion a year extra on the NHS, social care, schools and local government, shadow chancellor John McDonnell has said.
The extra spending would be paid for by tax rises for corporations and "the rich", set out in the "grey book" that accompanied Labour's General Election manifesto.
Mr McDonnell, who is calling on Chancellor Philip Hammond to end seven years of austerity with an "emergency budget" for public services next week, said even Cabinet ministers were calling for more spending.
He told BBC Radio 4's Today programme: "We've had some fairly strong messages from the front line of our public services about what's happening in health - the chief executive of the NHS telling us that there's a need for additional funding to avert a crisis.
"We've got head teachers, 5,000 of them, writing to the Prime Minister about the cuts, urging the Government to halt the cuts in our schools at the moment.
"For the first time - I've never seen this before - we've had the Government's adviser on tackling terrorism saying that that cannot be tackled if we keep on cutting our police officers on the beat in our communities.
"All of those messages now need to get to Government, and it's not just me saying this, it's Conservative backbenchers, it's even Cabinet ministers urging now that we start investing in our economy again."
Outlining how Labour would pay for its spending plans, Mr McDonnell said: "We said one way is that the Government has got to stop giving the tax cuts to the corporations and the rich.
"At the moment, the calculation now is that on corporation tax and capital gains tax, and some of these tax cuts to the rich, you're talking about £76 billion being given away during the life of this parliament.
"I don't think that's acceptable when our public services are in such a crisis."
Mr McDonnell said the Paradise Papers leak of 13.4 million previously secret documents, reportedly tying major companies and political figures to secretive overseas financial arrangements, showed more money could be raised from tackling tax avoidance.
He set out £6.5 billion in Labour's grey book that could be raised from clamping down on tax avoidance, based on advice from "tax experts".
But he added: "I cut that down from what was predicted - over £8 billion to £6.5 billion - because I thought we'd give it a bit of leeway.
"Now we know from the Paradise Papers it must be significantly more than that, even the Government now is going to have to address this."