What sort of culture capital are you specifically thinking about?
If you live far away from an urban centre you are going to struggle with access no matter how much cash you have. We are all aware cash helps a lot.
But, radio is free, radio 4 have loads of programmes on culture, introducing the general listener to quite niche art forms. A snooker final was on normal TV last night, world cup football last month, tennis and cricket in the summer.
There are usually local football (small teams) games almost across the country that don't break the bank and have great deals on kids tickets.
We can afford a big event once in a while, I suggested, to expand their tiny minds instead of panto next year perhaps we should go to see the Nutcracker in London instead, as it will cost, oh more than my car no doubt, I wanted full enthusiasm, I was met with a wall of horrified faces.
If you read interviews with modern culture creators you might be surprised how few were given piano lessons and opera tickets as a child.
You can find art and culture free in many many places, the wonderful world wide web can mean you can view or listen or watch almost any artist, musician, poetry ever created or study a movement or historical architecture without ever leaving your house. It is a great leveller. Kids with no access to agents can put out band music or spoken word direct and if they are good they will be liked.
You can take 1000s of photos on phones (photography used to be so expensive to develop), someone made a film on an iPhone a while back.
No perhaps you can't buy a bassoon.
Or go to the Albert Hall.
But I also think you can't blame a cultural desert for children nowadays on others who have more money.