Council leaders warned a reduction in government funding would lead to cuts in services which are already struggling.
Surrey County Council leader David Hodge said: "The reality for Surrey is we are facing significant demands on school places and on adult social care and children's services.
"When we have taken 40% out of our budget, it is extremely difficult to continue to do that."
Buckinghamshire County Council leader Martin Tett said a "tipping point" had been reached "where we can't just eat away at our back office services any more, we are going to have to do things in terms of home-to-school transport, cutbacks in a whole range of areas that people are going to really start noticing now".
He added: "We are going to have to make cuts of another £46 million in the next three years, and those cuts are going to be felt by people."
The government has pledged £275 million to help local authorities freeze council tax.
Local government minister Kris Hopkins urged councils to take up the offer of money, telling MPs: "All councils should be freezing their Council Tax in 2015 to 2016 and helping people with their cost of living.
"We are providing additional funding equivalent to a 1% Council Tax increase, to help councils freeze."
The latest government cuts in council funding "will push some authorities to breaking point", according to experts.
Graeme McDonald, director of the Society of Local Authority Chief Executives and Senior Managers (SOLACE) said: "This settlement reminds us that the financial challenge facing local government is immense.
"Government is beginning to recognise that councils have led the way on deficit reduction, but with cuts and demand increasing, fragility is beginning to show.
"The financial future of local services is unsustainable without a more ambitious plan for public service reform."
The cuts to council funding for the next tax year are the lowest since the coalition came to power.
Local government minister Kris Hopkins said that the 1.8% reduction would leave councils with "considerable total spending power".
No council will face a loss in spending power of more than 6.4%.
Mr Hopkins described the settlement as "fair for all parts of the country, whether North or South, urban or rural".
The bulk of local authorities' spending power comes from grants from central government, with around a quarter raised from council tax.
The amount of funding councils will get in central government grants will be cut by 1.8% in 2015/16, local government minister Kris Hopkins told the House of Commons.
Home Secretary Theresa May has announced plans to put a 28-day time limit on police bail, saying it "cannot be right that people can spend months or even years on pre-charge bail with no oversight
She has launched a consultation on the time limit that proposes it could only be extended in exceptional circumstances through an application to a magistrates' court.
I believe we need a statutory time limit in place to ensure people do not spend months or even years on bail, only for no charges to be brought.
Iconic red box used by the former Prime Minister to carry documents during his days as Secretary of State sold for £158,500.Read the full story ›
People should be deterred from being involved in criminal gang activities but those involved in so-called "joint enterprise" crimes should be sentenced for the crime they are guilty of, Sir Alan Beith has said.
The Justice Committee, chaired by the MP, has called for a review of the legislation, which currently contains a rule that in a joint enterprise murder, it is not possible to charge "minor" players with a lesser offence such as manslaughter.
An urgent review is needed into the so-called 'joint enterprise' legislation which was used to convict the men who murdered black teenager Stephen Laurence, a group of MPs has said.
The legislation currently contains a rule that in a joint enterprise murder, it is not possible to charge "minor" players - who did not encourage or assist in the crime - with a lesser offence such as manslaughter.
The Justice Committee wants that rule scrapped to stop people being sentenced to life in prison for murder when they were not directly involved in the killing.
Joint enterprise laws can apply to any offence, but has recently been used to prosecute murders - in particular ones involving gangs.
They have been invoked in a number of high-profile cases, including the 1993 stabbing of 18-year-old Stephen Lawrence in south London.
David Norris and Gary Dobson were convicted under the rules for his murder.