Police investigated seven crimes in three years that were reported in the street that is home to UK Prime Minister Boris Johnson and his Finance Minister, Rishi Sunak, Sky News reported.
London's police force did not say who reported the crimes but they referred to violent threats.
A man was jailed for two years last month after threatening to kill former prime minister Theresa May with a knife or gun.
Wajid Shah, 27, emailed Mrs May with the threat and sent similar messages to other senior politicians.
Mrs May said she was left “anxious and concerned” because of the explicit and repeated death threats.
A prisoner in June was also given a five-year jail sentence after sending death threats to Mr Johnson, Mrs May and female MPs.
Four crimes were reported from Downing Street in 2017, the year after the Brexit result, and two in 2019, the Metropolitan Police said after a freedom of information request.
"All the above crimes relate to malicious communications sent to Downing Street," it said.