The former PM converts

The former Prime Minister of the UK, Tony Blair converts from the Church of England to Catholicism.  I heard that his wife and children are Catholic. You may think "So what?", but this news means that for British people, it is very big news.  Hearing this news, I wonder whether the UK separate religion and politics or not.  I don't know.  Not only the UK but also America unites religion and politics in some cases.  I don't think that it is bad, but I've believed that separation of church and state is common sense, so I was shocked.  However Japan also unite religion and politics in some times.  As you know, Prime Minister visits Yasukuni Shurine almost every year.  I don't know and confuse the criteria of "separation of religion and politics".