I will have a trip to North London between Mill Hill Broadway and Mill Hill East in the coming weekend for a race. My coach has confirmed to me that there won't be other people coming with me so sharing a car is not possible. My final destination is not close to either of the station (1.6 km walking distance from Mill Hill East, 2.1 km from Mill Hill Broadway) so a connection on the 221 bus will be needed if I use public transport all the whole way.
It is possible to book fixed-time train tickets under £26 return using a railcard at the time of writing (split advance tickets between Bournemouth to Clapham Junction, and change to an Oyster to the Overground and tube avoiding zone 1 on a route using the Overground and tube only), however as there is uncertainty on when I can leave, I will need a flexible train ticket at least on the return.
I depart from Bournemouth and Google Maps suggest me to take the 12:27 train, the first departure where a super-off-peak ticket will be valid, however, it will involve an unofficial connection at Waterloo from the train to the tube. If only official connections are used, I will need to take the 11:59 train. Although semi-flex tickets are available on that train, it comes with a restriction "SW Railway Only" which means it is not flexible enough for my return need (as it's sometimes possible to change at Basingstoke for a CrossCountry train to arrive home earlier than waiting for the next SWR train), that means I will need an off-peak return ticket anyway, but it is much more expensive.
At the end I decide to buy the super-off-peak return to London Waterloo, change to the tube using Oyster and risk an unofficial connection anyway for my time-critical outbound journey (and take a taxi from Finchley Central or Mill Hill East to catch up the time in case I do run late) as the price difference between off-peak and super-off-peak is too attractive. As a result my journey will cost me approximately £41 and takes about 6:20 in total.
If I have a car, the trip is 367 km and Google Maps suggests 4:30 in total both ways. Therefore the car still gives a little bit of time advantage compared to using the fastest possible unofficial train connections, but I'm not sure if it will be more or less stressful keeping my car on schedule on the motorway or keeping my unofficial train connection on schedule at Waterloo. Assuming fuel economy of 10 L / 100 km and 144.3p / L, the fuel cost alone is already £26 (more expensive than taking the super-off-peak train or even the off-peak train), therefore it will not be worthwhile to drive a car based on the cost alone. Therefore, a car is only useful to squeeze every minute out of my trip, leaving my home at the latest possible minute for the race and returning immediately when the race finishes.
Therefore, it is utterly ridiculous to say that car travel is cheaper than train travel, even for a time-critical or a totally-flexible journey, as long as it is off-peak. The main use of a car is to squeeze every minute out of the trip, which is only possible if the corresponding train journey is not direct as in my case, and I suspect for anyone living in urban areas, it will be worthwhile to buy a car compared to using public transport as long as possible and use taxis / hire cars to make up times as long as all train journeys are in off-peak.