The annual council tax for a Band D property in Trafford this year was £2,120.84 while in Warrington it was £2,239.82.
Trafford Council said it had to ask for the extra support after the government’s Fair Funding Review left the area with a budget deficit of £24m.
Leader Tom Ross said the fact the area had asked for the increase two years in a row was a “difficult position” for the council.
In December, Warrington said it had the 37th lowest Band D council tax of the 99 unitary authorities and metropolitan boroughs in the country.
It said it had always made a decision to keep council tax as low as possible, but this was “no longer a sustainable policy”.
It added this was “particularly given the fact we are recognised for our sound financial management”, adding: “But we are not alone with other local authorities also reapplying.”
The council added: “It does mean that our efforts to increase revenue, save money and work towards financial sustainability are more important than ever and we are doing all we can to reduce our budget deficit.”
Denis Matthews, Warrington Council’s cabinet member for finance, said knowing about the permission for the increase gives the authority “important clarity” ahead of budget setting.
“We know that people are concerned about the impact of a potential additional council tax increase, and in that respect we have a lot to do, to restore trust with our communities,” he said.
“With the overall 7.5% increase, we would move from having a below average council tax rate compared to our statistical counterparts, to one that is more towards the average rate.”