Local councils should be allowed to levy local taxes but these should not replace the council tax, MPs have said.
Many pensioners have complained council tax is not fair
The power to raise tax locally was key to local democracy, the Office of the Deputy Prime Minister's Committee said.
Council tax should be kept providing it was improved along with council tax benefit, the MPs said after an inquiry into local government revenue.
Committee chairman Andrew Bennett said 2m households a year paid too much council tax to local authorities.
"It is crazy. Lots of pensioners are upset about council tax increases, but many of them are throwing money away," Mr Bennett said.
"It is little short of scandalous that central government is saving over £1.2bn of unpaid council tax benefit every year," he added.
The report said the government should stop tying councils down with "endless" targets and controls.
The committee also called for a new drive to ensure people took to the council tax benefits to which they are entitled.
Work and pensions minister Chris Pond said the government shared the committee's determination to see that everyone entitled to council tax benefit gets the help they need.
"As I told the committee, the Department for Work and Pensions is aiming for a 100% take-up rate."
He said he would continue to work with local authorities to improve council benefit take-up rate.
Ministers are currently carrying out a review of local government funding.
The Liberal Democrats have called for the council tax to be replaced with a local taxation system based on the ability to pay rather than the value of property.