It's true so far as it goes, it is the established church in England, the Dicoese of Gibraltar in Europe forms a part of the Church of England, but not the established church (its Diocesan is not entitled to a seat in the Lords for example).  Similarly Sodor and Man is not entitled to a seat in the Lrods, but does sit in some capacity in the House of Keys, the Channel Islands are also interesting, not part of the UK, in church terms they are an integral par of the Anglican Diocese of Portsmouth, and I'm really not sure of the consitutional position of the church there.  There's the added complication that the boundary between the Church of England and Church in Wales doesn't follow the civil boundaries, so some Welsh parishes are still in the Church of England, and some English in CinW.  Try and sumamrise that succinctly enough for the lead!

|But in generla terms we problem ought to deal a little more with the historical aspects, thoguh clearly much would belong in History of the Church of England, and also in discussing the formation of the Anglican Communion.