I get spoiled in DC, there are so many great museums and monuments that are open to the public without charge. I won't say they are free, because it costs a great deal of money to build and maintain galleries, museums, public buildings and monuments. Most of the ones that are open without charge, are paid for with tax dollars and donations.
We do this as a civilized society, in the words of James Smithson, to "increase the diffusion of knowledge." My life in this society is enhanced by others being exposed to art, science and ideas. As such we take on a society to support these institutions. Public institutions are not businesses, in the traditional sense of being run to make a profit. The profit or benefit, is a more worldly society. This is not to say that nonprofits should be carelessly or recklessly operated, over the years many have been. But they also fail to fulfill their mission if they are run on the model of a traditional business, making knowledge only available to those willing and able to pay for it. Those that need knowledge the most, are likely to be those least willing or able to pay for it.
So it strikes me as odd, when places like Westminster Abbey charge a substantial admission fee. I wouldn't mind tossing a couple of pounds on the box as I enter, but 16-pounds, almost $20 US, seems a bit steep, for maybe what I need most and am least likely to pay for.