As for the cost of rail travel - that's a complex one. If you take the business allowance for milage (currently £0.45 per mile - set in 2012, with inflation would now be £0.66) then rail fares aren't too bad.
...that's possibly not by accident, and still depends on you being flexible about times and/or being able to book in advance (so one ~200 mile trip I've looked up costs £134 return off-peak, but if you want to get there for a 10am meeting it goes up to £240). Then it's YMMV whether you're paying for car parking at one end vs. maybe needing a taxi to/from the station at either end.
...plus, as you say, as soon as you put two people in a car there's no comparison.
If you look just at the cost of petrol,
Thing is, once you have a car, depreciation, tax, insurance, service etc. are mostly "sunk costs" (with only a weak dependence on mileage) and petrol is the obvious extra out-of-pocket cost of any long journey. 0.45p a mile can feel like you're making a profit (even if you're not really). If public transport wants to compete on cost it's either got to be cheaper than the petrol cost or so consistently good that people can sell their cars.
Comparing with air travel is 'interesting' as there are significant subsidies for air travel.
Well, yeah, in the past I've paid less to get a flight to the Netherlands or Germany than to get the train to London. Thing is, unless you're a private jet type or have a mate with a Cessna, most internal British journeys are too short to justify having to get to/from an airport and hang around there for an hour. London to Manchester is about borderline. Consequently, there isn't much choice of routes & airlines trying to push internal air travel have come and gone like mayflies. When I have looked into it, the problem has been lack of planes, not price.
Also, however much we complain about the trains, my experience of
internal air travel in the US has been at least as unpleasant.