Some reports related to allegations of sexual abuse of people receiving aid, including children, the Charity Commission said.
Most of the 80 cases were historic, but seven were from the past year.
Aid minister Penny Mordaunt challenged aid agencies to up their game at the London meeting and said there would be "no hiding place" for predators.
"We will find you. We will bring you to justice. Your time is up," she said.
Reports that staff at British charity Oxfam paid for sex with prostitutes in Haiti after the 2010 earthquake have left the aid world reeling.
The sector has been further rocked by allegations that women in Syria have been exploited by men delivering aid for charities and U.N. agencies.
Mordaunt, who co-hosted Monday's summit with the Charity Commission, told aid agencies the government would not fund those that failed to meet its tough new "safeguarding standards" introduced on Monday.
Britain's Department for International Development (DFID) has asked 179 aid agencies to provide assurances regarding their operations, and confirmation that they have referred any concerns to the relevant authorities.
All have replied, but DFID is seeking further clarification from 37 of them, Mordaunt said.
The Charity Commission, which regulates charities in England and Wales, said 26 of the 179 organisations had made 80 "serious incident" reports.
These included "reports of allegations or actual incidents of abuse, including sexual abuse of staff, volunteers and beneficiaries, including children," it said in a statement.
DFID's beefed-up standards aim to ensure better protection of some of the world's most vulnerable people.
"Our standards will be world-leading. They will be tough and exacting," Mordaunt said.
The summit will brainstorm ideas around improving staff vetting, supporting whistleblowers and abuse survivors, addressing internal power imbalances, and creating an independent body to promote external scrutiny.
DFID also announced on Monday that an internal review that examined allegations of sexual misconduct by its staff showed there had been 14 substantiated cases since 1995.
The majority related to sexual harassment between staff members, DFID said. None involved sexual exploitation in exchange for aid.
A number of other cases are still under investigation, but DFID did not elaborate.
DFID's permanent secretary, Matthew Rycroft, told agencies they must "seize this moment ... to ensure we bring some lasting good out of this crisis".
The British parliament's International Development Committee also launched an inquiry on Monday into the sexual exploitation and abuse scandal.
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