The Church of England also known as the Anglican Church is the most important church in the United Kingdom. Especially outside England they are called Anglicans or Epispocals. Anglicans are between mainstream Protestants and Roman Catholics and vary from extreme Liberal Christians through to Christian fundamentalists.
History of the Church of England
The Church of England started in the 16th Century when King Henry the Eighth of England decided to divorce his wife and the Pope wouldn't agree to the divorce. Without that England would probably have stayed Roman Catholic.
Archbishop of Canterbury
The Archbishop of Canterbury is the leader of the Church of England and of Anglicanism worldwide. The Archbishop of Canterbury has far less authority than the Roman Catholic Pope and is always seen as a fallible Human being.
The Church of England is steadily losing influence and members to other Christian groups, other religions and to those with no religion in the UK. The Anglican Church is important as a world wide Christian organisation and may not be losing members elsewhere. In the United States of America Anglicans are called Episcopalians.
There is a strong tradition in the UK that the church doesn't interfere in politic, however the former Archbishop of Canterbury, Dr Rowan Williams felt so strongly that he has criticised the Conservative government,
(...) the Archbishop said the government was facing "bafflement and indignation" over its health and education plans: "With remarkable speed, we are being committed to radical, long-term policies for which no-one voted. At the very least, there is an understandable anxiety about what democracy means in such a context." 
Present Archbishop of Canterbury, Justin Welby has also criticised government policies that hurt Poor people.
As a civilised society, we have a duty to support those among us who are vulnerable and in need. When times are hard, that duty should be felt more than ever, not disappear or diminish. It is essential that we have a welfare system that responds to need and recognises the rising costs of food, fuel and housing. The current benefits system does that, by ensuring that the support struggling families receive rises with inflation. These changes will mean it is children and families who will pay the price for high inflation, rather than the government.