One in three English councils spent more on services in a year than they expected to, according to official data.
The total expenditure during 2016-17 for 113 councils came to just over £1.5bn more than was given in official estimates.
Councils said that in many cases they received additional funding that meant their budgets still balanced, despite big cuts in central government grants.
It comes as Northamptonshire County Council has introduced emergency spending controls due to "severe financial challenges".
Analysis of official budget data by the BBC England Data Unit found about one in three English local authorities spent more on services in 2016-17 than they expected to at the start of the financial year.
What are the main pressures on council budgets?
From the rising numbers of children going to school to a fall in the amount of money councils receive from central government, demands on local authorities are rising, while resources are being stretched.
The Local Government Association (LGA), the body that speaks for councils says over the next two years local authorities are facing a funding gap of £5.8bn.
The biggest pressure on council budgets is social care, which involves looking after vulnerable children and a growing older adult population.
Five years ago councils in England were spending slightly less than they had provided for in their social care budgets.
In 2016-17 local authorities spent £1.1bn more on social care than was in their forecast budgets.
Government data on "net current expenditure" represents what councils expect to spend on providing all services such as schools, care homes and housing, before they receive funding from central government to pay for them.
The fact that one in three councils spent more than they expected to last year does not mean councils are in financial trouble.
However, it does show many councils found demand on their services to be greater than they had anticipated.
South Hams District Council in Devon spent £6.6m more than was estimated, equivalent to 21% more than was forecast.
However, the authority stressed that once additional grant funding or income the council generated for itself was taken into account, it was left £45,000 over budget.
Selby District Council in Yorkshire, which spent £4.6m more on services than expected, said it was "sustainable now and in the long-term too".
A spokesman said: "Our accounts for 2016-17 and our arrangements for securing value for money have been given a clean bill of health by our external auditors."
Why is Northamptonshire County Council in trouble?
Northamptonshire is the first council in nearly two decades to issue a section 114 notice, which effectively stops all new expenditure. Only statutory services for safeguarding vulnerable people are exempt. The last one was Hackney in 2000.
Northamptonshire County Council says it currently has £608m in outstanding loan debts and £194m in Private-Finance Initiative liabilities.
The means the council's combined debts of £802m are greater than its planned budget spend of £706m.
Northamptonshire County Council also had the largest increase in spend on agency workers for social workers.
The Council says it has faced "unprecedented demand for local services for a number of years, coupled with reducing levels of funding from central government".
"The reliance on agency staff in social care is an issue faced by many local authorities across the country," a spokesman said.
He said the heavy investment in children's services came following an "inadequate" Ofsted rating in 2013 and that spending on agency staff had dropped after recruiting more social workers.
You might also be interested in
What does the government say?
The Ministry of Housing, Communities and Local Government says that over the next four years councils across England will get real terms increases in their budgets.
And when asked in the House of Commons whether he knew of any other councils in financial difficulty, the local government minister Rishi Sunak said: "It would be inappropriate to give a running commentary on every conversation I have with local councils, but the department keeps in constant contact with councils and we keep the situation in constant review."
An independent inspector has been appointed to look at the financial situation of Northamptonshire County Council, which is expected to report back by 16 March 2018.
Correction 14 February 2018: This article has been amended to better reflect the issues raised by this data, which relate to forecast budget versus actual spending rather than overspending.