Does the Church of England regard itself as responsible for the behaviour of the general populace? Today, the Church of England has released an apology for a statement they made.

In response to people now entering into civil partnerships, rather than traditional marriage, the C of E made a statement suggesting such partnerships should be 'abstinent friendships' or, in other words, platonic relationships. They are now 'back-tracking' on that previous statement.

My question is not about that issue, itself.

My question is about whether the Church of England regards itself as a regulatory authority over the entire populace. 

Or are its directions only made to persons within the Body of Christ, that is to say, those who show repentance and faith and who are followers of Jesus Christ in doctrine and in conduct ?
The Church of England cannot and does not of itself regulate the behaviour of the general British population. Church laws apply only to clergy and to members of the church, and sanctions against ordinary church members are limited to church matters. In other words an ordinary member can be punished only by things like expulsion from the church. Even then such sanctions are used extremely rarely.

The Church of England has some small contributory part to play in British government, in that twenty-six of its bishops have the right to sit in the House of Lords (the upper chamber of the British parliament). It is very rare that their influence is decisive. There are other minor ways in which it plays a part - for example some schools are administered by the Church of England on behalf of local education authorities.

Along with most other Christian groups, the Church considers that there are moral standards that apply to all people, and it is the church's duty to uphold those moral standards both by example and teaching.