Our local Baptist chapel has this issue, the Anglican Church not so much. Mostly because people find it a way of meeting nice families for their kids to hang out with.
Interestingly, that seems to be bucking the national trend, Rhi. OK, the Baptist congregation may be a fairly 'high' Baptist one, and the Anglican a fairly evangelical one.
Peter Brierley's Christian Research group are finding that the congregations that are fading fastest are the non-evangelical (and in the CoE, the Anglo-Catholic) ones. In other words the ones who have a high proportion of cultural, rather than religious attendees.
But I'm not really talking so much about churchgoing for religion. I'm talking about the culture - I'm sure we all know atheists who attend choral music programmes in church, admire church architecture and religious art. I even know someone who attend carol services every Christmas just because. I think if this kind of cultural Christianity was suppressed, as it was in Russia, there would be a groundswell of support. It's not about religion, but identity and expression.
I would disagree it would be a groundswell of support. From where I stand and from what I've seen happen, it tends to be that the non-cultural members are released from the constraints often imposed by the often middle-class 'what can I get out if this place' members that stop many churches actually doing what Christ asked his followers to do - care for the sick, feed the poor, support the disadvantaged, and share the gospel, etc. I've attended churches where the 'culturals' regularly voted against anything that smacked of social action and of reaching out to, and including, the needy and disadvantaged.