Federation leaders warned that the public will be "out in droves" on July 4, with one fearing a return to Accident and Emergency departments resembling "a circus full of drunken clowns" at weekends.
Metropolitan Police Commissioner Dame Cressida Dick said her force has been planning for July 4 "for some time" and that the public will see "a lot" of officers on London streets.
She told the BBC Radio 4 Today programme: "We're planning, we've got extra resources in place, we're talking to people in every way we can think of, we are absolutely prepared.
"You will see a lot of police officers out on the street. There will be a lot more ready should people be out of order, should people get violent. But I'm not predicting that at this stage."
Tim Clarke from the Metropolitan Police Federation, that represents officers up to the rank of chief inspector, said he feared this weekend "could be anything but a 'Super Saturday' for police officers".
He went on: "The challenges they face this weekend with pubs and restaurants reopening and many people predicted to travel across the country to see family and friends will make this weekend perhaps as busy as policing New Year's Eve.
"People will be coming out in droves and if we have nice weather again this weekend it will be a significant challenge with the further relaxation of Covid-19 guidance.
"This could have been mitigated by waiting until Monday to further relax the Government guidelines to us all - but as always, policing and police officers will do the best we can in the challenging circumstances."
London has seen tensions flare during recent protests and a number of unlicensed music events.
Dame Cressida said: "My message is, if you're coming out on Saturday, be calm, be sensible. Look after yourself, look after your family.
"We are still in a global pandemic which is affecting this country very obviously. People need to be sensible."
Brian Booth, chairman of West Yorkshire Police Federation, warned that alcohol fuels crime and puts more strain on the emergency services.
He said: "Police officers are right to have concerns about this weekend and Government restrictions being lifted based on our experience of people's behaviour changing when alcohol is involved.
"We have more violence, street disorder, sexual assaults, missing people and injured people who may need medical assistance. All of these impose significant strain on policing and our colleagues in the NHS.
"Having seen the effect of fast food drive-thru outlets in West Yorkshire opening, and some of the public behaviour which followed, my concerns are heightened purely due to alcohol and the issues this brings.
"Prior to the Covid-19 outbreak, local A&Es on Friday and Saturday nights were at times akin to a circus full of drunken clowns. We do not need this once again.
"It is known that alcohol lowers inhibitions and I truly hope the vast majority of public maintain their common sense, remembering we are still living under the cloud of Covid."