That is just too simplistic - there are plenty of journeys where there is no rail equivalent and there are others where rail is the mode of choice. You cannot just agglomerate them all and make one assumption about shifts in mode. Everyone in the industry is expecting a fall in passengers except possibly where rail competes with air.
Whilst it's a fairly simplistic view, not least as I do understand that rail isn't a viable option for many trips, the view that road won't also be impacted by this as well is more simplistic.
Whilst rail will see a change in use, mostly from fewer people commuting, road use will also see similar changes.
There are several reasons why the ownership of multiple cars (and to a lesser extent any car) will see a fall.
Firstly we have all got used to buying stuff online, with one of the main problems with this being that people aren't at home to get the delivery. Well WFH will overcome this problem.
Next up is that we've seen what our towns and cities look like without cars and seen through the smokescreen of the claim that most vehicles are delivery vehicles. This is because deliveries are up significantly yet traffic is down significantly. Traffic congestion is down to the private motor car and those who wish for there to be better towns and cities as well as those who want more active travel now have a brilliant case study to point to as to what having less traffic can look like on the roads.
Another factor is that people will lose jobs (that's just the way it will be and whilst it will be terrible for those it impacts there's no point sugar coating it), as such there's not going to be the economy to support the purchasing of so many cars. As such there will be some who will have no other choice but to use public transport to get to work. Especially if that work is of unknown length. You certainly would buy a car for a job which may only last 6 weeks before you are then looking for a new job. Especially if some/all of the work being done is WFH.
Therefore if money is tight people may start to actually look at what their cars truly cost them and may decide that they can't afford the luxury of a few pounds a day to have their own space. Especially if the numbers of days which a car is being used falls due to working from home, which can significantly increase the daily cost of travel for work.
Given that office workers are likely to be amongst the last let back out, there's a good chance that there'll be some who let their car leases lapse to then consider if they truly need a car once they are back at work. Especially if they are still being to encouraged to work from home in 6 months time (personally I wouldn't be overly surprised if some social distancing isn't still in place in 2 years time whilst a vaccine is still being distributed, as it's likely 12 months before it can be shown to be safe, with then another 12 months of vaccinations at 110,000/day to get to 60% of the population, to deliver it much faster, bearing in mind that the whole world will also want it, would be fairly tough to achieve, as to deliver it within 6 months would be the best part of 1/4 million vaccinations a day probably at a time when the NHS was seeing more normal use of hospitals and GP's so would probably not have as many spare resources to deliver such a massive program).
There's another factor which is often overlooked, car ownership is generally higher in the older population, with many of the younger generations not owning cars. Likewise the numbers of miles each car drivers had been falling. Combined, this has been changing the way the country gets about. This virus is likely to further impact this.
Now whilst car usage could spike whilst there's the perception to need to avoid others (i.e. people driving to avoid public transport), such a spike is likely to be short lived. Not least as the roads could grind to a halt. As many urban roads see congestion during peak hours, however see little congestion during the school holidays when traffic volumes drop by ~10%. This is because it takes fairly small amounts of extra traffic to overload junctions. It also doesn't take very much about above the normal congestion to bring about gridlock. Therefore if we saw extra road traffic (maybe even just from the extra delivery vehicles) it could make driving nearly impossible. Therefore long term an increase in driving at the expense of public transport isn't going to work.
One final point, what's going to power those cars? Long term it's not going to be the ICE, the problem is that EV's aren't overly green. They are less efficient than battery trains, which in turn are less efficient than EMU's.
However even leaving that aside the mining of the materials to power and provide the batteries for those vehicles is generally an ecological problem.
It had been said that our total electrical supply, to be able to be provided by sustainable power sources, needs to stay broadly the same (if not fall), charging a loaf of EV's is going to result in a very large spike. As such the age of the private car is, unless something changes fairly soon, likely to be coming to an end (at least as we understand it).