In Britain church membership of any kind has no direct financial implications for the state. However, the Church of England (Anglican) uses baptismal records to try to justify its massive financial privileges as the state church ― and even its political privilege of having 26 of its bishops sit in the Upper House, where they can help veto democratically-passed laws.
Leaving the Church of England would seem to have few implications for church-state separation. That's because the Anglican Church, like the Catholic Church, counts you in, no matter what you do after getting baptised.
It has good reason to use baptismal statistics as a tally for church membership, since if defections were reflected in official figures, it might have difficulty claiming its present privileges. 
A Times investigation established that a figure of 25 million baptised Anglicans in England was used by the Wakeham Commission in reform of the House of Lords when drawing up its recommendations. The World Council of Churches also allocates seats to the Anglican churches of the UK based on a figure of more than 25 million baptisms. And the 80 million figure used to describe membership of the worldwide Anglican Communion includes 26 million baptised Anglicans in England.
Were any of these to be adjusted to reflect the Sunday attendance figure in England of 1.1 million, the Church of England's argument for 26 bishops in the House of Lords would risk being undermined, its representation at the World Council of Churches reduced and the official size of the Anglican Communion cut by nearly a third. 
1. Linda Woodhead, "Time to get serious", Church Times, 31 January 2014. http://www.churchtimes.co.uk/articles/2014/31-january/features/features/time-to-get-serious
2. Ruth Gledhill, "England: Christian asks to be 'de-baptised'", The Times, 20 March 2009. http://www.timesonline.co.uk/tol/comment/faith/article5934198.ece)