The perceived dithering and divisions of church officials over the protest camp outside St Paul's in London have claimed a second major scalp with the resignation of the cathedral's dean, the Right Rev Graham Knowles.

The dean – whose job is sufficiently senior that a replacement must be approved by the Queen – announced that mounting criticism over the cathedral's handling of the situation made his position "untenable".

In a statement read on his behalf to the media at the Chapter House, opposite St Paul's, Knowles said: "In recent days, since the arrival of the protesters' camp outside the cathedral, we have all been put under a great deal of strain and have faced what would appear to be some insurmountable issues.

"I hope and pray that under new leadership these issues might continue to be addressed and that there might be a swift and peaceful resolution."

Last week the St Paul's canon chancellor, Giles Fraser, stepped down after the cathedral's governing chapter voted to begin possible legal action against the Occupy the London Stock Exchange camp, in place now for 16 days. A part-time cleric also resigned.

Cathedral elders have faced criticism not just over the possibility that force and violence will be used to evict the camp, but for the decision to close the cathedral for a week over health and safety concerns that remain unclear. The church has also experienced wider condemnation for failing to properly and publicly agitate on the excesses of finance and global banking until prompted to by the camp, part of a burgeoning global movement.

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The bishop of London, Dr Richard Chartres, who spoke to activists at the camp on Sunday, told the briefing he had been asked by the chapter to assist the cathedral until Knowles's replacement was found.

Chartres said he wanted St Paul's to find a place in modern public life as pivotal as that it had during bombing of London in the second world war, when it was a symbol of Blitz defiance.

The chapter had said they "would not condone the use of violence in effecting any expulsion" of campers, he said. However, he added, the legal action would continue and the position could change: "Who knows what is going to happen?"

The first step in what is likely to be a lengthy legal battle to remove the anti-capitalist camp from outside St Paul's was beginning later on Monday afternoon when officials were due to formally hand activists a letter requesting that they pack up their tents and other belongings.

A Corporation of London spokesman said the letter, which was still being drafted, was likely to ask that the Occupy the London Stock Exchange protesters move within 24 or 48 hours. Activists have been camping outside St Paul's for several weeks in protest at the perceived excesses of bankers and the global finance system.

Legal officials from the corporation, which owns some of the land around St Paul's, said they would distribute several copies of the letter in the camp.

If the activists do not comply, which appears almost inevitable, then the corporation's lawyers will most likely start court proceedings on Wednesday under the Highways Act, seeking an eviction. This process could take several months, lawyers have warned.

The letter will point out that there is no objection to a 24-hour protest at the site, on the western edge of the cathedral, but that the presence of more than 200 tents plus assorted marquees providing food, information and other facilities means the thoroughfare was blocked.

Announcing the plan to take court action after a meeting on Friday, Michael Welbank, the councillor who chaired the meeting, said: "Protest is an essential right in a democracy – but camping on the highway is not."

The Occupy camp ended up on the site, which is part owned by St Paul's, on 16 October after an initial plan to base itself at nearby Paternoster Square, the private business and retail development housing the London Stock Exchange, was thwarted by police action.

The cathedral has backed many of the camp's aims, but on Friday said it supported legal action.

A protester at the camp, Spyro van Leemnen, said any response to the letter would be decided at a general assembly later in the day. The movement makes decisions democratically, through mass meetings.

The group has promised to remain at St Paul's in the long term and spread to other areas in the City. A "spillover" camp at Finsbury Square, further east, set up a week ago, is now thought to be near capacity. It is believed that protesters will target a third site later this week.