Owning a motorcar only makes sense if you can somehow incorporate usage of said car into your lifestyle, as an alternative to the transport system.
With an increase in telecommuting, home delivery of groceries and so forth, the 'base load' of travel that justifies a car is much diminished. With a general desire to do more stuff at home, combined with a lack of destinations for the foreseeable future, the leisure excursions will be also reduced. The car is a burden that many households will forego, and was a trend before this outbreak.
Government requests that people use alternatives to the transport system have, as we have already seen, the same success as requests that motorists switch to the self same transport system prior to the outbreak. The modest gains there took decades which suggests it will probably take another couple of decades to slow down and turn round the supertanker which was already steaming in the direction from private motoring towards professional transport systems. The electric cars which we rely on to be a practical alternative to buses and metro in cities are not yet at the mass market stage.
All this taken into account, I'd wager that the motor trade is rattled to a much greater degree than the transport services.
Indeed, cars are fairly expensive with high up front costs, so once you fall below about 4,000 miles a year it tends to be very hard to justify the expense (unless you are proper rural and not just in a location with a population of 4,000 to 10,000 which can often have fairly reasonable facilities, which when paired with online shopping allow a significant number of tasks to be undertaken without needing to travel more than a few miles).
Given that 85% of people live in urban settings (a settlement with over 10,000 people) then there's really quite a large potential for there to be many fewer cars than there currently are.
As examples (and I know not everyone will fall into this these examples, but there will be quite a few for whom it could be a viable option):
Couple where both work and both own cars, their work patterns changes so that they WFH 2 days a week. This then allows them to each share a car, other than one day when they both go into their offices and one of them uses public transport to do so.
A family with a stay at home patent, who has a car for the various activities (swimming, football, dance, etc.) the parent in paid employment then works from home 2 days a week allowing the stay at home parent
to use the other car and reduce their car ownership to one from two.
A family where both travel long distances to work and pay a fair amount in childcare, by one of them stopping working (or more likely taking on a local part time job) they could reduce their costs significantly (one car rather than two, much reduced child care hours, fewer brought coffees and lunch, etc.).
The vast majority of people who own a car would be paying in excess of £2,000 a year when you add up all the costs of car ownership. £450 fuel, £250 insurance, £150 servicing & MOT, £140 VED, £60 tyres & other consumables, £50 parking, £900 purchase costs (including loan repayments), many paying significantly more than this. Whilst it's possible to reduce the costs a bit below this probably not by much.
However if you need £2,000 to run your car you actually need to earn more than this to be able to have the take home salary to pay that much, unless you aren't earning enough to pay any tax (although this has to be your income, in that if your other half who is a higher rate tax payer is paying for it then the money they have to earn to pay for it is about double the cost).
Few really appreciate just how much a car actually costs them to run.
The other thing to consider is that whilst fuel may not be much for each mile that you travel, that quite a few people do a lot of miles which they could do by other means. Such as to and from school (half a mile each way every day is 150 miles a year, given that my 2 year old can walk over a mile and it's not really much quicker than walking then there's not really much to be gained from doing so).