A good question to which there are good answers. First, large expenditure on local roads by the local authority is often financed by a grant from Central Government. Second, local authorities have their own revenue stream from motorists in the form of parking charges and fines. I have to pay to park outside my house. Third, if a house has its own garage, the council tax on that property will be higher. Fourth, in London we have what is fraudulently called a congestion charge.
Incidentally, many local authorities, particularly in London, spend very little on roads for the benefit of motorists. They spend a lot on cycle lanes and low traffic schemes but neglect fundamentals such as road surfaces and drains.



You've decided that everything that London does is also done everywhere else.
Not the case at all!
Government grant funding to LAs is being constantly cut. They are increasingly retaining Business Rates, but that revenue isn't road-user specific.
Birmingham has a few residents parking schemes, the outside of the city centre ones are £19 per year.
Fines is less than £5m per year.
The highways budget is ~£100m per year for Birmingham, with the central gov grant covering half of that.
But central gov grant funding is being cut; https://www.expressandstar.com/news...est-midlands-roads-cut-by-around-40-per-cent/
Own garage doesn't mean the council tax will be higher than all other properties. Plenty of roads full of terraced houses that are a higher council tax band than semi's with a garage.
Cycle lanes, LTNs etc cost very little to implement, have very low maintenance costs.