Westminster Council has objected to plans for 128 new boxes since January, including 80 from Maximus Networks Ltd.
Birmingham and Manchester councils say that the boxes are effectively little more than advertising boards.
They say they cannot stop them as planning permission is not needed, just an Ofcom licence.
Maximus Networks said it was offering "a truly useful" public service.
Three cities have had 301 applications for new phone boxes in 12 months - 158 in Westminster, 104 in Birmingham and 39 in Manchester.
Councils can object to Ofcom's approval of the boxes but only on two grounds: location and design.
A Department for Communities and Local Government spokesman said it was considering the matters raised by councils.
Each Maximus Networks box would provide 1.3m x 2m of advertising space which does not need local authority consent.
Westminster Council said the boxes, which the company planned to install on Oxford Street, Victoria Street and Baker Street, would offer no wi-fi or internet connectivity.
"This scheme will create ugly and unwanted advertising space," Councillor Richard Beddoe said.
However, Maximus founder Ashley Smatt said: "We believe what we have planned will be the envy of the world.
"There are currently around 66,000 calls a week from phone boxes across the UK and we believe there is a demand for this."
Councillor Daniel Astaire, of Westminster Council which rejected another operator's proposal for 48 boxes on Tuesday, said companies "are trying to make a quick buck" with "ugly hoardings on some of our most iconic streets".
Birmingham City Council deputy leader Ian Ward said "open access wi-fi and widespread mobile phone use" made the kiosks "redundant".
But he said he anticipated more coming, "because city centres offer a highly lucrative market for advertising and there's no restriction on how many can be installed".
Ofcom said it had no evidence Maximus had breached any obligations but it would "be concerned" if permission was "used to provide advertising space under the cover of a largely unwanted public call box service."
Councillor Pat Karney, of Manchester City Council, said the only people he had seen using phone boxes "are drug dealers, particularly around the Piccadilly Gardens area".
Redundant kiosks are increasingly being put to inventive uses, from defibrillator storage to miniature art galleries.
There are about 46,000 remaining public kiosks across the UK including about 8,000 traditional red ones.
About 2,500 of those in England are listed, according to Historic England.

The Tories have promised £4bn extra but this equates to a £1bn rise in real terms, the independent think tank says.
When growing pupil numbers are taken into account, investment per pupil will fall 2.8% by 2022, the IFS says.
Labour has pledged to increase spending per pupil by 6% over the course of the next Parliament.
The IFS says this would require an increase of around £4.8bn in real terms or 2017-18 prices.
The Liberal Democrats' plans protect per pupil spending over the course of the Parliament in real terms at the present level (for 2017-18).
This would require £2.2bn extra investment.
Presently, the schools budget is £40bn a year.
Luke Sibieta, associate director at the IFS, said: ""The commitments made by each of the main parties would imply quite different paths for school spending in the next Parliament.
"Labour would increase spending per pupil by around 6% after inflation over the course of the Parliament, taking it to just above its previous historic high in 2015.
"Proposals from the Conservatives would lead to a near 3% real terms fall in spending per pupil over the Parliament, taking it back to its 2010 level."
The analysis of the headline figures comes as parents are preparing to hold events in different areas of England to highlight the cash crisis facing schools.
The IFS has previously said schools are currently facing the first real terms cut for 20 years.
Head teachers have been complaining of the tough decisions they have had to make about staffing and resources.
Councils are fighting plans for hundreds of new "ugly and unwanted" phone boxes while they seek a change in the law.
[NEXT_CONCEPT]
A new Conservative government would leave schools in England worse off financially than they currently are, the Institute for Fiscal Studies says.