If the protesters refuse to clear the area specified in the notice, the corporation said it would begin legal proceedings at the High Court to seek their eviction.
After the deadline passed, a City of London Corporation spokesman said: "We have been in talks with the protesters we have been yet to reach a suitable agreement.
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The BBC's Stephen Dowling at the protest camp
As the deadline for the eviction neared, the Occupy London Stock Exchange leadership organised a range of speakers to voice their concerns.
There was a pensioner urging the youthful movement to keep at it; a cleric saying the demonstrators had to take their cause into the mainstream; and fellow protesters from occupations that have brought dissent to the streets of New York and Madrid.
As the St Paul's bell chimed, the protesters threw their arms up in the air in a "Silent Scream" protest - a quiet outburst of sorts in keeping with the occupation's non-violent approach.
"We therefore have decided with some regret that we need to resume legal action.
"The communication channels are still open but now in parallel with the court action."
Naomi Colvin, an Occupy London spokeswoman, said: "We're not planning on going anywhere soon and certainly not at the behest of the City of London Corporation.
"We're not remotely concerned about legal action.
"We are aware of our legal position, the likely time frame and we have a great legal team on board. Why would we possibly be worried?"
The Occupy movement has said its protest aimed to highlight the issues of inequality and corporate greed.
A statement from the Chapter of St Paul's said: "We recognise the local authority's statutory right to proceed with the action it has today.
"We remain committed to continuing and developing the agenda on some of the important issues raised by the protest."
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