Scotland's biggest council is warning it could lose as much as £133m per year from its budget under the SNP Government's plans for replacing council tax with a local income tax.

Labour-controlled Glasgow City Council has calculated the tax would have to be set at 4.5 pence on every taxable earned pound. But the impact of reduced revenue if Scottish ministers cap the fund at 3 pence, as they plan, that would leave the city £60m adrift from its current budget.

If the UK Government then withholds any of the council tax benefit currently coming to the city's local authority, that would leave a further £73m gap. It reckons those twin problems threaten between 6% and 11% of the cost of running services.

Finance Secretary John Swinney has said central government will pay grants to councils to sustain services while capping the national rate at 3 pence, reckoning that should cost £280m per year nationally.

But the Glasgow figure of a £60m gap suggests the £280m estimate for the whole of Scotland could be a substantial under-estimate of what is needed to plug the funding gap.

The budget hole left by the end of council tax benefit in Scotland, running at £400m, is acknowledged by SNP ministers as a reason the whole policy could founder.

They say Whitehall should release that money for reallocation by Holyrood, but the UK Government responds that if there is no local income tax, there is no reason to pay compensating benefit.

Glasgow's city treasurer, Stephen Curran, has drawn up a report detailing the costs of the local income tax and concluding the council should oppose it. It says the city authority will draw up alternative plans for council taxation reform, recognising concerns about the current system. Labour at Holyrood has not yet done that.

The Glasgow analysis suggests that, from more than 6200 people who used the council's online calculator, 72% would be financially better off if the tax is capped at 3 pence, while 21% would be worse off. Lowest income households would not benefit.

Responding to Councillor Curran's report, Glasgow SNP MSP Bob Doris claimed the city council had "shot itself in the foot" by showing the majority of people would be better off. "No amount of fiddling the figures can hide the fact that evidence from council tax payers from across Glasgow shows 72% of Glaswegians will see their tax bill reduced by the introduction of a local income tax," he said.

Glasgow LibDem MSP Robert Brown said the Labour council was missing the point about local income tax, as the council is already 85% dependent on central government grants and that would be adjusted to ensure fairness.

"When some pensioners pay six times as much of their income as council tax as the richest people, you know that something has gone very wrong with fairness in Scotland," he said.

LibDems support the SNP plans in principle, but do not back the nationally-set rate. Even with LibDem MSPs, the SNP administration is still two votes short of the majority it needs to pass a council tax reform bill.

The local income tax plan also faced criticism this week from employers' lobby the Confederation of British Industry. It claimed the change would undermine enterprise and the economy and is viewed with "deep disquiet" by its members.

It was seen as adding to employers' administrative payroll costs, it could undermine the mobility of workers between Scotland and the rest of the UK and make it harder to attract higher-paid talent and investors into Scotland. There was also criticism of the lack of detail behind the proposed system.