Millions of households in England are facing council tax rises above the normal limit, after the government allowed six areas to bypass a 5% cap on increases.
Usually local authorities with social care duties can only raise council tax every year by up to 4.99% without a referendum, while others can increase it by up to 2.99%.
But Deputy Prime Minister Angela Rayner has confirmed that Bradford Council will be allowed an increase of 10%, while Newham and Windsor and Maidenhead will all be allowed a 9% rise - Birmingham, Somerset and Trafford can increase their bills by 7.5%.
Rayner said the increases were crucial to "prevent these councils falling further into financial distress".
She said: "We recognise the importance of limited increases in helping to prevent these councils falling further into financial distress – but we have been clear this must be balanced with the interests of taxpayers."
The government blocked several councils from raising taxes above 4.99%, including Hampshire, which had asked to be allowed a 15% increase.
A statement on local government funding also confirmed that councils will have access to more than £69bn this year - a 6.8% increase in cash terms compared to 2024-25.
The agreement means no council will see a reduction in core spending power.
More than £2bn of this will come from direct grant funding above revenue received from council tax.
The announcement also confirmed councils will get an extra £5bn to manage the cost of increases to employer National Insurance contributions.
The top-up brings additional funding for next year to around £2bn, on top of £1.3bn announced at October's Budget.
Specific allocations to mayoral combined authorities remain at zero, meaning they are expected to generate funding through other means.
Local Government Association chair Louise Gittins said council finances remain "extremely challenging" and the extra money next year "still falls short of what is desperately needed".
She said: "This financial year therefore remains extremely challenging for councils of all types who now face having to increase council tax bills to bring in desperately needed funding next year yet could still be forced to make further cuts to services".
She called for a "more sustainable future funding system" as well as "significant and sustained increases in overall funding" for councils in the upcoming spending review.