But changes meant to resolve the problems are likely to open up a new front in a bitter ideological row within the Church.
It all comes after the committee that appoints new bishops could not come to agreement on two recent occasions, leaving the posts unfilled.
Insiders have told the BBC they felt the main issue was differing views on same-sex unions, with some selectors thought to feel unable to appoint someone with an opposing stance.
Elephant in the room
The urgent leadership meeting of the House of Bishops on Wednesday was called in response to a letter signed by 13 bishops about an apparent breakdown in the way the Crown Nominations Commission was working.
After a recruitment process, that panel is meant to recommend a member of clergy to fill a vacant bishop or archbishop position.
The same commission will have a hand in selecting the next Archbishop of Canterbury, possibly in early 2026.
But the inability of the panel to come to a two-thirds majority in agreeing on a candidate means that, to date, no one has been appointed to be either the Bishop of Carlisle or Bishop of Ely.
Although the process is meant to remain confidential, leaks suggest one major problem is intransigence by members of the panel on one issue that is currently bitterly dividing the Church; blessings for same-sex couples.
Early last year, equality activists were left upset when the Church said it would not consider a vote on whether it would conduct same-sex marriages. Nevertheless its general assembly (Synod) voted to support a form of blessing for same-sex couples.
There has since been vocal opposition from conservatives within the Church and it is an issue that has already led to breakaway splits in the wider Anglican Communion, particularly in Africa.
Domestically, divisions have become increasingly bitter, with factions having formed and acrimonious and heated debates every time Synod convenes.
Several bishops have told the BBC they feel factionalism over the issue of same-sex unions is a key factor in the problems the Nominations Commission is having in making appointments.
There are also conservative members of the selection panel opposed to the idea of women bishops, another issue that has long divided the Church.
Neither of these underlying influences was addressed directly at the emergency meeting of the House of Bishops, where the focus was all on the process of selection.
“There was a lot of fear in the discussion,” one senior bishop who did not want to be named told the BBC.
“The elephant in the room was about power and who exercises it and the Church’s continued inability to address openly and honestly matters of gender and sexuality,” the bishop said.
Instead, the bishops looked purely at procedural solutions that might alleviate the current crisis, ultimately voting to pass new measures.
They included the removal of the “secret” nature of the ballot to decide on a new bishop, and also a lowering of the vote threshold and allowing the presiding archbishop on the panel an extra vote if there is still deadlock.
But the vote by these, the most senior members of the Church, was not unanimous with a 27-9 split. A result along the same lines as the numbers among the group known to support and oppose same-sex blessings.
Those bishops opposed to the selection panel changes said in discussion that the new moves risked looking like a power-grab by the archbishops and could be perceived as being undemocratic.
But the measures passed also still need ratifying by the wider Church at its General Synod. That assembly is where the splits are likely to be thrown open much more plainly.
Recent meetings have often been characterised by acrimony and deep division. It is division that now appears to be having an impact on the workings of the Church.