Police officers could start letting violent suspects go if they do not get the backing of the public, a federation leader has warned.

The chairman of the Metropolitan Police Federation, Ken Marsh, spoke out after video footage appearing to show two officers locked in a violent struggle as they tried to make an arrest was shared thousands of times on social media.

The footage, taken in south London on Saturday, appeared to show a male officer being dragged around in the road as he tries to stop a suspect in a white tracksuit running away.

A second man, wearing a grey tracksuit, seems to take a run-up before aiming a flying kick at a female officer, who then lies dazed in the road clutching her head, feet away from a passing bus. She appeared to have tried to use incapacitant spray on the pair but to no effect.

A member of the public wearing a motorcycle helmet helped the male officer in the struggle, but several cars went past without stopping.

Play Video 0:33 Police in violent struggle in south London – video

“Are we now in a society where, if we think we can’t detain somebody, we just let them go? It’s just not worth it,” said Marsh, who represents thousands of police officers in the capital.

“We’re going to come to a point where we’re going to start pushing messages out to our colleagues: ‘Risk-assess it dynamically and, if you think you can’t detain a person, just let them go.’

“We don’t come to work to get assaulted and, if we’re not going to be backed up in what we’re doing, then what is the point?”

Last year, Marsh criticised what he saw as a loss of respect for police as it was revealed that nearly half of the officers he represents want more armed officers on the streets and a significant majority backed the routine issuing of Tasers.

“If you look at the last two to three years, the number of assaults on police are going up unrecognisably. The average constable doesn’t hold the same authority. When I was a child, you didn’t dare blink at a police officer,” Marsh was quoted as saying at the time.

A new law is due to come into force this month that doubles the maximum jail term that can be handed down for attacking a member of the emergency services from six to 12 months in prison.

The law covers police, prison officers, custody officers, fire service personnel, search and rescue services and paramedics.

Speaking when it was given royal assent in September, the prisons minister, Rory Stewart, said: “Assaulting prison officers or any emergency worker is not just an isolated attack – it represents violence against the public as a whole.

“Every day these public servants do extraordinary work on our behalf, and they must be able to do it without the fear of being assaulted. Our message is clear – we will protect our emergency services and violence towards them will not be tolerated.”

Speaking to the Daily Telegraph on Monday, Chris Bryant – the Labour MP who sponsored the new legislation – said: “The bill will only be effective if there are enough police officers to implement it and there is the will to act. We need to have the police, the prosecutors and the courts all lined up and taking it seriously but they also need government backing.”

Scotland Yard said a man was due to appear at Wimbledon magistrate’s court on Monday, having been arrested and charged with with assault causing ABH and assault on an emergency services worker. He was also charged with driving without insurance and driving other than in accordance with a licence.

Officers are still searching for two other men in relation to the incident.

The two officers were taken to a west London hospital. A female officer sustained head injuries and a male officer suffered cuts. They have both been discharged.

The issue of violent crime has been high on the agenda in recent months and official data showed a 14% increase in police-recorded homicide offences across England and Wales in the year ending March 2017. But the Crime Survey for England and Wales, thought to be the best measure of trends in crime, suggests no recent change in the amount of violent unlawful acts.