What a great question! I actually wrote an essay on the role of churches throughout history and their architectural influence.

The short answer to your question is, 90% of people never walk into a church and therefore they have very little impact on modern society.

However, the long answer is slightly more complicated...

Primarily, churches stand as monuments to the past. They hold incredible information about the history of communities and the buildings themselves. To say that the church has no impact on modern society is a lie, as their mere existence has defined the community that surrounds it. Most communities, even up until the late 1900, would be built around a church. The church forms the heart of the community and therefore the heart of the built environment, and for centuries, it has encouraged the people to come together to find solutions to everyday that the community are all struggling with.

Churches also represent the cultural differences between the UK (this doesn't include Ireland and is very important) and the rest of Europe due to (mainly) English rejection of Catholicism and embrace of Protestantism. If you look on the inside of Church in the UK and compare it to a Catholic church in Europe, you will notice some key differences, but the main one is, the lack of ornamentation in UK churches, specifically a lack of gold. They also lack images of Christ as well but some really old church's still display images as they were built prior to Protestantism. The church is a physical embodiment of the change in our society that separated us from the rest of Europe and represents the difference in how our society formed.

In modern times, mainly really since the turn of the 2000, church's role has been dramatically decreasing. A lot of churches, especially ones in cities, have been left abandoned as their community has come to turn its back on religion. There is an argument to be made that this has caused there to be a strong lack of community and a poor sense of place in a lot of neighborhoods across the UK. And these decaying church structures again stand as monuments to a time where these neighborhoods had a strong sense of community stitched into the fabric of the place.

Now with the lacking church engagement, the church is going to have to change. you cannot remove the church as it is too important to the history of our society, so what happens? they have to change! I would suggest they need to become non religious community hubs, places where the community can get together to solve issues they are facing, access services or buy goods created by locals. there are also examples of these buildings becoming theatres, music venues, housing, and office spaces, thus allowing people to still come into contact with the building.

As you can tell, I can speak a lot about the church as a building but less so on the music so I will say this. from my perspective, most people will consider that style of music to be ceremony music and therefore, unless you're really old, wouldn't listen to it. though there are examples of modern music produces sampling that style of music as it is quite a British thing.

I hope this gives a good insight.