So what is it about UK (actually, probably English rather than Welsh/Scottish/NI) culture that is different to other countries/regions with a better public transport culture? Why do people in parts of the UK object to, presumably, taxation being used to fund such things, when some other parts of the western world don't have such a problem?
The countries/regions that seem to be able to do it properly include the stretch of the continent from Belgium down to Austria, plus, judging by TT-ONR-NRN's trip reports, much of the more populated parts of Australia (NSW round Sydney, Victoria round Melbourne) too. These countries/regions presumably have the majority of people using their own cars to get about, like us, but also presumably don't seem to object so much to the funding of integrated public transport.
Well that is a controversial question for this forum! Trying not to stir up too much of a hornets nest, I guess it is because of the different influences that UK culture has been subjected to over the centuries, compared to those other countries. From a distance we all appear similar, but there are just so many subtle differences of thought, process and outlook. I am not so sure that the Welsh/Scottish/NI outlook is that much different to England - their provision and integration is similarly pretty woeful compared to your comparator countries, and they have different funding arrangements. Even adjacent countries with greater shared history than us (France/Germany) pour monies into public transport but have completely different integration outcomes.
I suspect the way our modern transport grew up is a further influence - our railways were private enterprises long after all your comparator countries had been nationalised (or were always state owned), and the bus industry was allowed to (generally privately owned) flourish much more freely (rather than being railway owned and/or highly regulated subservient to the railways). Apart from a very few examples, they have never been integrated.
There is no one explanation, just a combination of influences and history that make up the current situation, and you can take your pick as to which are the important or otherwise.
The position today is that there is a huge swathe of 'middle' England with multiple cars who have little interest in public transport (none in buses apart from to take their kids to school, and themselves from airport terminal to a plane on the apron, and only trains to London) and, outside of the major cities, an aspiration of anyone not in 'middle' England to move up there ('middle' being an economic/cultural state rather than geographical). Which explains the fact that there is little or no political or grass roots impetus to invest/support public transport. Plus, of course, plenty of vested interests not to rock the status quo!