Demonstrators at the “Unite for Freedom” march hurled objects at police including bottles.
Two of the injured police officers were taken to hospital and five people were arrested in the clashes.
A number of pictures have emerged of police officers with blood running down their faces.
People flocked to the capital on Saturday to protest against lockdowns and the idea of vaccine passports.
Protesters held placards reading “Do Not Comply”, “We Want Our Freedom”, “Covid-19 Vaccine Holocaust”, and: “No To Vaccine Passports”.
The Home Secretary pledged to double prison sentences for anyone who attacks emergency service workers.
Ms Patel tweeted: “Our brave police are the best of us and should not be the target of senseless violence by a criminal minority for just doing their job.
“I am getting tough on these thugs and will be doubling the sentence for assault of an emergency worker.
“I wish the officers a speedy recovery.”
The Home Secretary shared a series of pictures showing bloodied officers following Saturday’s rally.
In one, a distressed officer with a cut to her head is helped by colleagues after being injured.
Another picture shows an officer with his face and tunic covered in blood from a head wound.
Following Saturday’s clashes Met Police Chief Supt Roy Smith said in a now deleted tweet: “What sort of reasonable human being grabs a police officer’s baton and then appears to punch her in the face?
“There should be widespread condemnation of this violence towards officers yesterday.”
Footage taken at the rally showed maskless demonstrators goading officers and chanting: “Shame on you”.
As the officers attempt to move the crowd on, objects are thrown into the air and one protester lets off a canister of blue smoke.
One clip shows officers crouching down to shield themselves as demonstrators
A Met spokesperson said: “Eight officers were injured as they worked to disperse crowds in Hyde Park.
“Missiles including bottles were thrown in small pockets of disorder. Two officers were taken to hospital.
“Thankfully, they are not believed to be seriously injured.”