Officers in St James’s Park in Westminster became aware Prof Whitty was being accosted by a group of men at around 7.20pm on 27 June.
The Metropolitan Police said it had checked the chief medical officer’s welfare are the time of the incident, and that he had not suffered any injuries.
A video of the encounter was widely shared on social media.
Officers subsequently reviewed footage that emerged after the incident and the matter was referred to the public order crime team. Enquiries continue, detectives said in a statement.
Prof Whitty, who has a leading role in devising lockdown restrictions and regularly appears alongside Boris Johnson at coronavirus press briefings, has been involved in a number of encounters with members of the public during the pandemic.
Last month, he was confronted on a street in Oxford by a man accusing him of lying to the public about the virus, while in February a man accosted him near parliament. Both incidents were filmed on mobile phones.