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He said if both measures went ahead, drivers would face an average extra bill of £630 a year.
Speaking at the Scottish Parliament during a debate on the workplace parking levy (WPL), Mr Briggs said: “The majority of motorists in the Capital will very soon face the burden of having to pay to park outside their homes and at their place of work.
“The city council stated that they have an estimated 32,500 eligible parking places across the city.
“The estimated £14 million revenue expected to be raised by the council is based on £428 per space, which is the current price in Nottingham, the only UK city were the tax has been brought in.
He said as one o the lowest-funded councils in Scotland, Edinburgh had been left little option but to use the car park tax to raise vital additional resources.
He told MSPs: “Motorists in Edinburgh are set to become the highest taxed in any part of Scotland and the UK with SNP-Labour-Green councillors not only planning to introduce the car park tax but also a huge roll-out of paid parking zone permit areas across the Capital.
"We all know the cost of living is going up, making it harder for hundreds of thousands of people to break even every month. Food prices have been on the rise and pressures on energy costs are seeing bills increase.
“With the car park tax and parking zone permit charges motorists in the Capital will face on average additional set of car taxes of £630 after May’s council elections if SNP-Labour-Green councillors are returned.
“Also, people outside of Edinburgh travelling to work in the Capital from the growing communities of West, East, Mid Lothian and the Borders and Fife will have to pay Edinburgh council this charge, which will be of no benefit to them in their own local authority.
“The cost of an annual parking permit in Edinburgh is already on average, £202.91, which is the third highest in the UK and £82 more expensive than London. Overall, the average cost of a permit in all cities in the UK is £103.08, almost half that of Edinburgh.”
He said the WPL was an indiscriminate tax, which would impact most on low-income families and price people out of owning a car.
“With the cost of living pressures facing families across Scotland this is the wrong policy at the wrong time and one which will hit the poorest in society.”
Edinburgh transport convener Lesley Macinnes said the administration would be considering WPL guidance carefully before bringing forward any proposals, which would be subject to widespread public engagement.
“None of us can afford to ignore the challenges in combating negative impacts of climate change and we must look to all sorts of solutions to meet those challenges. We need to be open to radical measures which will help us tackle the huge contribution transport makes to health-related issues as well as air pollution and congestion.”