I thought that secularism meant the separation of church and state. Thus, the state is (theoretically) blind to a person's religious convictions and an individual is therefore able to exercise freedom of conscience/observance.

In this the US still mostly adheres to this. Not perfectly nor without prejudice, but mostly you can recognise the intention.

Although the UK does favour certain religions, even granting some of them representation in the House of Lords (for goddess alone knows what reason), by and large, our laws are indifferent to religion even if it is as not as much as we like. I was very pleased to discover last year that I had not previously known that Michael Howard (Tory leader 2003-5) was jewish, as it had been something of such little consideration to his position that it had never been mentioned.

Only Blair made a point of letting us know he was religious, just so he could then let us know he "didn't do god".

keep to the Fen Causeway