The officers were injured while attempting to escort a police motorcyclist through the area at about 12.30pm on Saturday, the Metropolitan police said in a statement, The Guardian reported.
Video footage from the protest posted on social media shows shoving between police and protesters.
Thousands of protesters had gathered from 12pm in Parliament Square, from where they marched through the capital, with the hashtag #londonprotest trending on Twitter.
Among those marching with protesters were Gillian McKeith, former host of Channel 4’s You Are What You Eat, and Maajid Nawaz, the LBC radio host.
At around 3pm, a group of protesters stopped outside a shop on Regent Street, police said.
They began “directing abuse” at people inside and egging the shop until police intervened, ending the incident, the Met added. No injuries were reported.
A further incident occurred at about 4pm when beer cans and flares were thrown at officers on Whitehall.
The force said officers were also subjected to “abuse and physical violence” elsewhere on Whitehall – leading to several more officers sustaining minor injuries. No arrests were made.
According to a report in the Express, the demonstration was organized by a coalition of groups including Take a Stand London, Save Our Rights UK and The Great Reopening.
Many of those marching held placards that had been printed by a group called Together, which hosts an online petition against vaccine passports, mandatory vaccinations and the government’s summary introduction of COVID powers that has been signed by more than 167,000 people.
The protest had its critics online, however, with some observers suggesting that by gathering together, those taking part would make lockdowns more likely by increasing transmission of the virus.