Figures seen by The Telegraph this summer showed that Britain’s yearly council tax intake could rise by £17.6bn by 2030, because of annual increases in the levy.
The rise would add another £500 to average council tax bills by the end of the decade.
Mr Brown’s comments come amid fears that Mr Burnham and John Healey will raise property taxes in the autumn Budget next month.
The Prime Minister hinted in July that he would reform or replace the council tax regime to “create some fairness” for northern England.
He has complained that there are people in Greater Manchester who were paying “much higher” council tax than people in London who may live in “much larger homes”.
Mr Burnham has previously expressed support for a land tax, an annual charge based on the land a property sits on, rather than the building itself.
This would go some way to remedying what the Prime Minister claims is a regional mismatch, increasing bills in London and the South of England, while lowering them in other areas. The idea has the support of more than 100 Labour MPs.
Others have suggested a “proportional property tax”, which would replace both council tax and stamp duty with a flat 0.48pc annual charge on the value of a home.
Economists and policymakers from across the political spectrum agree that stamp duty weighs on the property market by preventing Britons from moving.
‘You’ve got to be very careful’
Elsewhere in the interview, Mr Brown warned that imposing a wealth tax could cause high-net-worth individuals and entrepreneurs to leave the country to avoid paying the levy.
He said: “If people can move their wealth, then if one country has a wealth tax and others don’t, then there’s obviously a huge opportunity for it to be evaded and avoided.
“I think you’ve got to be very careful about these taxes. I’ve always said that it takes time to persuade people of the need for change.”
Mr Brown added: “The truth is that in Britain income is taxed quite heavily, and wealth is taxed not so heavily as in other countries.
“You’ve got capital gains tax of course, as well, which is another tax. And so you’ve got these wealth taxes. And I think you’ve got to look at the consistency and the coherence between them.”
It came after Lord O’Neill of Gatley, the former chief economist at Goldman Sachs, who advised Mr Burnham during his election campaign, urged the Prime Minister not to impose controversial wealth taxes.
A Treasury spokesman said: “The Chancellor is fully focused on his priorities, to boost business, help with the cost of living and support people in every postcode.
“As has always been the case, the Chancellor will set out decisions at fiscal events, rather than routinely commenting on rumour, speculation or proposals.”
