There is no doubt the AutoTrader have an axe to grind on this, and like all journalism its coloured by the views of those writing and the people behind them paying their wages.
There probably is an increase in demand, but I doubt that much of it is due to the current rail problems. A lot of people held off from changing their vehicle during covid for multiple reasons, and so there is undoubtably a bit of a backlog.
This doesn't detract from the fact the situation with regard to the railways isn't serious, industrial unrest, failing TOCs, and a disinterested and weak government. I personally don't believe that line closures will happen, I think that is still politically unacceptable, but service cut backs and a cutting back (off?) of investment will happen.
You cannot rely on railways at the moment over a large part of the country, and people will make alternative arrangements, bus, car, fly, etc. and this will increase demand for cars but bearing in mind the proportion of rail journeys to other modes of transport this increase will be very small, and masked by other larger impacts from other events.
There's a LOT of empty space in this country, 85% of the population live in urban areas (population of over 10,000), most of the rest likely live in places between 5,000 and 10,000.
As such why would public transport try and serve places with (say) 1,000 people or fewer when it'll never compete well?
Of course if everyone living in such places never ever used rail or would make hardly any difference to passenger numbers, even though such areas make up most of the area of the country.
I live in a rural settlement (population circa 9,000), it's surrounded by countryside with almost no one in it until the next villages, whilst one is almost abutting it, it's still for quite a lot of farmland and tiny hamlets for the next 2 miles, whilst in another direction there's a small village about 1.5 miles with a school and then it's almost 6 miles until you get to the next place with a school. That's in a location about an hour from London.
For myself this wasn't the case. I stuck with public transport for 20 years. I could drive but I hated it. I wanted to support the buses.
However over the past twenty years the once good bus service of 4 buses per hour which took 40-45 minutes end to end has deteriorated into an hourly service (when it runs) which takes over an hour from end to end. The other bus services we had to other towns (which were tendered) have all been reduced from hourly, to exactly one bus there in the morning and one bus back in the evening.
The bus companies have left us high and dry, the nearest train station that I used was reached by using one of those withdrawn tendered services. So the knock on effect was that I also stopped using the train because the nearest station been four miles away is too far to walk to.
So finally in frustration, I've given up and bought a car. Once the car was bought and insured, it's proved cheaper to run and far more convenient.
I won't be using the buses again.
Which is why cutting public transport is a foolish way of trying to save money, as if many did that or urban areas would grind to a halt. However whilst there's a lot of the UK which is rural, there's still a need for some bits and rail services to serve them.
Indeed with a drop in new car sales of 75% compared to pre Covid levels there's a risk that car purchasing is going to be expensive due some time (just 6 years of that with 1% year on year growth in car numbers and to get the average age of cars back you need to add 17.5% more cars to the fleet).
I think the unions are cutting their own necks. The government are warning a whole generation could be put off rail travel.
At the end of the day rail travel is heavily subsidised by the tax payer, it is, to a large extent, a public service and is not a free market business like most others. Rail employees are by and large well paid, we are all having to tighten our belts and most of us do not have the option to go on strike for more money anyway. Our only choice if we're unhappy with our wage is go and get another job !
Pre Covid railway support was about £7bn, circa £1bn of loan costs (which would be needed even if the railways didn't exist), £3.2bn was for enhancements print out at about £3bn.
If we could close the railways, we'd need to spend a significant amount more on road improvements so that goods could still get about without significant extra delays.
The best way to reduce the gap between income/expenditure is to do the trains, maybe with some targeted cuts, however a blanket arbitrary 10% off may actually harm the economy so much that it actually costs the government more.
This is certainly true in not negotiating with those striking (chances are an extra 1/2 a percent or less of a change in conditions could be enough to bring it to the end.
Especially where TOC's are insulated from loses from the strikes, this means that the level of government support is likely to be higher than it needs to be as there's fewer people paying to use the railways. This is then made worse by people being put off using rail.
However rail use in the last 12 months matched 2009, rolling forwards the last 6 months matches 2011, a 5% increase in each of the next 2 quarters would bring the year total to 2012, maybe even 2013.
Without strikes we could even see rail use higher still.