To what degree does the Church of England consider the Genesis creation account to be metaphoric? Does the Church of England generally consider the Genesis creation account (first couple of chapters) more metaphor than literal history?
The Church of England has not taken a stand on the simplified 'creation versus evolution' debate. Many people investigating this have reported being unable to find a clear positional statement from the CofE, and there are quotes from church leaders stating that they believe there is no official position. This is an example. The church has made pronouncements stating that a belief in evolution is compatible with Christian faith, but that does not mean that those who believe in a literal creation are excluded from the church.

From personal experience, members of the CofE, both laity and clergy, take a wide variety of positions on the matter. The recent Archbishop of Canterbury has stated his personal acceptance of evolution, but does not see the Genesis creation stories in opposition to that.

So to answer the direct question, the Church of England makes no definitive pronouncement on how much of Genesis is 'metaphorical', but the general position of most of its leaders is that at least the timeline of the first three chapters should not be taken as literal history.