A motion seeking to remove the monarch and prime minister from the process of appointing diocesan bishops will be debated by the General Synod of the Church of England on Monday
The motion, to be put forward by the Rt Rev Colin Buchanan on Monday on behalf of the Southwark Diocese, calls for a more "participatory and open church procedure than is currently possible".
The issue of the government's involvement in the affairs of the church has become a sensitive one because Mr Blair will have the final say on who succeeds Dr Carey when he retires in October.
Dr Carey is attending his last Synod as the Archbishop of Canterbury.
Dressing down
If the Synod began a move to take over the job of selecting bishops, it could be seen as threatening the church's established status.
The Archbishop of Wales, Rowan Williams, who is thought to have been recommended by a selection commission as the next Archbishop of Canterbury, would like to achieve greater independence for the church.
The Synod, the church's parliament, meets several times a year to discuss church business and strategy; this session is being held at the University of York.
Subjects still to be debated include marriage law, the conflict between Israelis and Palestinians and the type of clothing worn by clergy during services.
It will be suggested that vicars should be allowed to swap ornate robes for ordinary clothes to take services, including Holy Communion.
Its backers say ornate clerical regalia is intimidating and acts as a barrier to potential church goers.
On Tuesday, delegates will debate the House of Bishops' report on marriage in church after divorce.
The debate will build on church reports "in accepting that there are circumstances in which a divorced person may be married in church during the lifetime of a former partner".