Announcing this year's tax rise of 1.85 per cent, leader of the Tory-run council Mike Fisher said "we wouldn't have to make this decision" if the borough received the same money per head as some neighbours "with less need".
He singled out northern neighbour Lambeth as a borough that Croydon increasingly resembles and yet receives far more government funding per head.
This year, Croydon will receive £102.9 million in its main (Formula Funding) Government grant, compared to Lambeth's £195.2 million, despite Lambeth being home to nearly 100,000 fewer people.
Croydon does, however, receive nearly double the grant than its Outer London neighbours, with Bromley this year getting £49 million and Sutton getting £42.5 million.
The annual figure is calculated using a complex formula that takes into account each borough's population and their needs, although questions have been raised by ministers nationally about the accuracy of the data and the fairness of allocations.
Councillor Fisher said: "We are now more diverse than Lambeth. If you look at the most recent census, we have a lower average annual income for households in Croydon than in Lambeth, and many other indicators show that Croydon is in more need than Lambeth. But if we received the same level of grant per head as people in Lambeth, we would get an extra £140 million per year from government.
"Now, if we got that I could cut council tax this year by 94 per cent. So I suppose my challenge to government is, give me the chance, give me Lambeth's grant per head for a year and I will show you what I do with council tax."
Cllr Fisher added he had been "making the case to the Government" and was "bitterly disappointed" it had not overhauled local government finance beyond changes to business rates.
From April, councils will be allowed to keep 50 per cent of the business rates they collect, rather than the whole pot being redistributed across the country.
Local government secretary Eric Pickles said he hoped the measure would put an end to a "begging bowl mentality, with each council vying to be more deprived than its neighbour."
"Our reforms will allow councils to stand tall, and reward them for supporting local jobs and local firms," he added.
Cllr Fisher said: "That is their answer if you like to some of these issues, but it cannot be right when you have a borough like Croydon which is now more diverse than the borough next door, but we see such a huge difference in funding. We will continue to make that case."
This year's announcement of a council tax rise comes amid steep cuts in Government funding to local authorities. A cut of £26 billion has seen councils' spending power drop by 1.7 per cent.
Tony Newman, leader of the Labour opposition, said calls for more funding for Croydon had cross-party support.
But he added it should not distract from "wasteful" spending on projects such as the new council headquarters and what he described as a high bill for consultants.
"Yes it is an issue," he said, "but for Councillor Fisher effectively to be seen to be blaming his own government is not acceptable because he has taken the [spending] decisions in the borough which I have highlighted."
He issued an open invitation to Cllr Fisher to form a joint delegation to the Government to make Croydon's case.
"Croydon politicians, regardless of party, would always agree that want to see more funding for Croydon," he added.
This year's council tax is to rise by 1.85 per cent – although total bills could go up by 1.2 per cent if a cut to the London mayor's share is approved. The increase, with the mayor's reduction, will see taxpayers paying between 23p extra and 68p extra per week depending on the value of their homes. Band D taxpayers will be paying an extra £17.56 per year (34p a week) if the mayor's share is cut, with their total annual bills rising from £ 1,456.83 to £1,474.39. Council leader Mike Fisher said the increase will raise £1.3 million for the council each year and was needed to protect frontline services amid huge cuts to Government funding for local authorities. He said: "I think to protect investment in schools, in school improvement, in a whole range of council services, that is an increase which most local taxpayers would be prepared to fund." In raising the tax, Croydon Council joins about a third of councils nationally rejecting the Government's offer to help pay for a freeze. Nathan Elvery, acting chief executive of Croydon Council, said they had refused the offer mainly because the funding would only last for two years. "Rather than deferring hard decisions for a few years, it is actually time to make those decisions now," he said. Councillors will meet on February 26 to approve the budget for 2013/14. The London mayor's share will be decided at a Greater London Assembly (GLA) meeting the day before. Some Assembly members want to keep his share the same rather than reduce it, so there is more money for fire and police services. Steve O'Connell, Croydon and Sutton's GLA member and Croydon Council's cabinet member for finance, said he would vote for the reduction. He said: "The mayor went to the polls on a pledge to cut his share by ten per cent over four years and he is starting that process. "It is a fair debate to be had but our view is that there is significant investment in the police and the fire services."Council Tax by Band: 2013/14 Croydon Services; GLA; Total bill Band A: £ 780.92; £ 202.00; £ 982.93 Band B: £ 911.08; £235.67; £1,146.75 Band C: £1,041.22; £ 269.33; £1,310.55 Band D: £1,171.39; £303.00; £1,474.39 Band E: £1,431.70; £370.33; £1,802.02 Band F: £1,692.00; £437.67; £2,129.67 Band G: £1,952.31; £505.00; £2,457.31 Band H: £2,342.77; £606.00; £2,948.78