Hundreds of people gathered in Centenary Square on Saturday for an event called 'The North Unites Rally', which appeared largely peaceful until some protesters tried to break through a human wall of police officers.
Some of the protesters attempted to cause disruption by making their way to the Jacob's Well vaccination centre. No vaccination centres or testing centres were affected by the demonstration.
Nine police officers were injured and more than 13 people were arrested.
Chairman of the West Yorkshire Police Federation said: "My colleagues did a tremendous job on Saturday, striking the right balance between peaceful protest and the unique position of policing in a pandemic.
"It is truly difficult position to be in, on one hand people are peacefully protesting about the infringement of their civil liberties and on the other hand, in the midst of a pandemic, the public expecting us to keep them safe.
"It is like being between a rock and a hard place.
"Regardless a few attendees overstepped the mark and were dealt with swiftly and arrests were made, unfortunately a few officers were injured in the process, but none of them seriously.
"It is yet another example of the difficulties that my colleagues face in these unique times."
West Yorkshire Police revealed four people have been charged following the demonstrations on Saturday. They include a 35-year-old man from Keighley who has been charged with holding a gathering of more than 30 people outdoors in a Tier 4 area; two men, aged 45 and 39, from Bradford and a 41-year-old man from Wetherby, who have been charged with participating in a gathering of more than two people in a public outdoor area in a Tier 4 area.
They will appear at Bradford Magistrates' Court on June 11.
Out of the other people arrested, West Yorkshire Police confirmed:
A man arrested on suspicion of a public order offence has been released under investigation;
A woman arrested on suspicion of affray and assault on emergency worker has been released under investigation;
A man arrested on suspicion of assault on an emergency worker has been released under investigation;
A man arrested on suspicion of affray and assault on emergency worker will receive no further action;
A man arrested on suspicion of assaulting an emergency worker has been given a conditional caution;
A man and woman were given fixed penalty notices for participating in a gathering of more than two people in a public outdoor place outside the area;
A man arrested on suspicion of conspiracy to commit violent disorder has been bailed pending further enquiries;
A man arrested on suspicion of violent disorder and assaulting an emergency worker has been bailed pending further enquiries;
A man arrested on suspicion of dangerous driving and obstructing a PC has been bailed pending further enquiries;
A man who was arrested with assaulting an emergency worker has been bailed pending further enquiries;
Three people arrested for failing to provide details were issued with COVID fines.
Detective Chief Inspector Andy Farrell of Bradford District Police, said: “Our investigation doesn’t end with what happened on Saturday – as a Senior Investigating Officer I am leading an investigation and reviewing the evidence obtained during the demonstration.
“On the day a number of people were arrested, and police officers were injured as they helped to keep the people of Bradford safe. Thankfully none of those officers were seriously injured.
“It is important to remember that we remain in the middle of a deadly pandemic and although some of the national restrictions have been relaxed today, public safety is and always will be, our top priority.”