Footage from the protest showed a woman appearing to pick up medical equipment and papers from the site and then dumping them in a nearby bin.

Another demonstrator allegedly knocked down a sign, and another man apparently threw a couple of traffic cones.

Dozens of people were seen in the video, including some who were holding anti-vaccine placards and shouting anti-vaccine slogans.

Police said that "where criminal offences have been disclosed, we will take swift action and bring offenders to justice".

Among those addressing the crowd at the demonstration was Piers Corbyn, the brother of former Labour leader Jeremy Corbyn.

Health Secretary Sajid Javid said he was "appalled to see Piers Corbyn and his mob threaten NHS test and trace staff who are working so hard to keep people safe.

"This kind of vile behaviour is unacceptable," he added.

Home Secretary Priti Patel said she was being updated on the police investigation.

She added: "It is more important than ever that people have their vaccinations and booster jabs.

"And it is completely unacceptable that conspiracy theorists are intimidating and harassing those administering tests or delivering the life-saving vaccine programme.

"The police have my full support to take swift action where necessary."

Ben Everitt, the Conservative MP for Milton Keynes North, said of the protest on Twitter: "What a bunch of d***heads."

"Nobody deserves this at work," he added, as he paid tribute to staff and volunteers who "do an amazing job".

Mr Everitt expressed his hope that the police had got the evidence they needed to "bring these morons to justice".

One person, Dominic Dyer, said they were unable to get a PCR test because of the protest, tweeting that Mr Corbyn and "his anti-vaxxers rabble" had gone to the site to "threaten staff and destroy equipment".

Boris Johnson visited a site delivering jabs in the town on Wednesday, where the prime minister said 90% of those in intensive care with COVID had not had their booster vaccine.

Thames Valley Police said in a statement: "Thames Valley Police is aware of an anti-vaccination protest that took place in central Milton Keynes this afternoon.

"Where criminal offences have been disclosed, we will take swift action and bring offenders to justice.

"If anyone has any information or wishes to report they can do by calling 101 or online quoting reference 604 29/12/2021."