I think there are so many stumbling blocks when it comes to the drive to push people onto public transport.
In an ideal world, more people would use public transport but there are quite a few barriers which make this less likely in the UK, unless things change. Namely, public transport is often inconvenient and unreliable, expensive, and not particularly pleasant environment to be in. That's not to say the system doesn't work for some people- clearly it does, and some areas have better transport infrastructure and links than others too. And some people don't have any choice but to use public transport (or they'd have to walk or cycle).
However, for some people public transport is not going to be viable, or only viable sometimes- e.g. those who live rurally; people who have certain disabilities or are frail/elderly; those who require to have a car or van for work either because they have to be mobile (e.g. vet, GP) or because they have to be mobile and also carry large volume of equipment/parts (e.g. plumber, joiner); and some shift workers, would all be good examples.
I could not rely on public transport, it wouldn't work (even if I overlooked the fact that I become very travel sick in buses and can only travel facing direction of movement on the train). For a start, I would have to walk several miles to get to the nearest village to catch a bus. That bus comes max 4 times per day (Mon-Friday)with first bus being about 7:30 and last arrives in about 8:30PM. There are even fewer buses at the weekend/Sunday and public holidays being worst. If you work shifts, it can be impossible to get to work early enough due to bus times and quite probably won't be able to get back after work either. The journey itself takes a very long time- at least an hour (sometimes longer, depending on the route) to get to the nearest town- but only about 25 minutes drive by car. Then you factor in that depending on where in town you want to go you may need to get another bus (or two) and this adds in yet more time and increases the cost. And lets face it- the fares aren't cheap especially not if you are taking a family it is going to be even less cost-effective.
If you had to drop a child at school or nursery before work, and collect them afterwards, it would be very difficult and probably quite stressful.
Our local town has a train station- but not especially close to any bus stops or the bus station, so if you've got luggage and came by bus it's a trek lugging that about- and it can be a total nightmare to co-ordinate the bus and train times. Generally, it would mean a long wait at the train station. The train routes aren't always the most convenient and often at least one change is needed which can be a pain if the trains aren't running to time, and that's not infrequent. Train fares are very expensive. And to add insult to injury, they often run late, aren't usually the cleanest/nicest places to be and you're not guaranteed a seat.
Given the above, I very rarely use public transport. I frequently wouldn't be able to get to work on time (or even close), nor would I be able to get home. Flexi-time is not really an option for me due to the nature of my job. Even if I could somehow get into work/get back on time using the bus, the commute would be at least an hour each way (more often 1.5 hours each way) instead of 25-30 minutes. For this privilege I would pay at least as much as my car and travel in less than comfortable/clean transport on many occasions. I may not even get a seat. It's not rocket science to see that for people in my position public transport won't work.