From what I understand, it's every separate council which sets its own tax rate.
The mayor has a precept added because he is responsible for police, fire, etc., and TfL.
"Mr Goldsmith said he would be able to freeze the precept - about £276 a year for a Band D property - because he had secured a deal with ministers to protect police numbers at 32,000.
“I believe we can go further, but I’ve not promised things in my manifesto that I’m not absolutely certain I can deliver,” he said.
The Mayor’s precept is worth £767 million a year, with £567 million going on the Met, £138 million on the London Fire Brigade and £69 million for services including transport and City Hall itself."
So whatever you have read, Kahn cannot set the bands himself.
Where did you read that? Goldsmith's leaflets?
Presumably if Goldsmith has secured a deal to keep police numbers at 32,000, that will apply to any mayor. They cannot say that will only apply if you vote for Goldsmith.