Prime Minister Andy Burnham has ruled out scrapping stamp duty, after reports suggested he planned to get rid of the tax.
It comes as Hartlepool's Labour MP Jonathan Brash has long called for major changes to the council tax system.
Mr Brash recently told the i Paper that "wholesale reform" of council tax is needed.
He said: "Council tax is one of the most unfair taxes in Britain, and nowhere is that injustice clearer than in towns like Hartlepool."
He has previously highlighted that band A homes in Hartlepool pay nearly 2.5 times more council tax than similar properties in Westminster.
During a visit to Portsmouth, Mr Burnham told reporters that regarding a stamp duty scrap: "that won’t be happening."
However, he did pledge to "make taxation fairer" as part of wider fiscal reform.
Mr Burnham recently criticised the "unfairness" of the current council tax system and acknowledged that "big decisions" lie ahead.
Speaking on BBC Panorama, he said: "There are people here in Greater Manchester who pay a much higher council tax than people living in much larger homes in London.
"So the chancellor before, Rachel Reeves, was right to start to reform council tax to create some fairness there in relation to people in homes that are of much greater value, who haven’t seen their council tax go up over the years because of the failure to revalue the banding.
"So that’s an example of something that I think was right and fair."
During his Portsmouth visit, Mr Burnham said: "I removed VAT off electricity bills, said we would do that, and that will come through later in the year.
"We are looking at how we take that little bit of pressure off people’s shoulders, reduce the cost of living."
Conservatives have criticised any move to replace council tax, arguing it would raise costs for many.
Shadow housing secretary Sir James Cleverly said: "Andy Burnham and Labour are just looking for more ways to tax middle England, and raise taxes on people’s homes.
"Replacing council tax and stamp duty with a new house price tax would not be a tax cut for hardworking families - quite the reverse: people across England would end up paying more."
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