Becky Dobson, 27 and brothers Jason Hill, 32, and Stuart Hill, 30, died in the incident at 5.20pm local time on Saturday.
Ellie Milward, 29, Jonathan Udall, 32, and Jennifer Barham, 39, were airlifted to University Medical Centre in Las Vegas, Nevada, along with pilot Scott Booth, 42, according to Arizona Central.
Dramatic images of the crash site show the wreckage lying at the bottom of a canyon, engulfed in flames.
One picture appears to show a female survivor, wearing jeans and a white top, fleeing the scene as the fire rages behind her.
Local media reports claim it took rescuers more than eight hours to get to the survivors and they were not airlifted from the scene until around 2am on Sunday.
Jonathan Udall from Southampton is currently being treated in hospital.
Witness Lionel Douglass told ABC News: "I had taken my phone and I was zooming in to see if I could see anybody and a lady walked out of the flames and I just lost it."
He said he saw the helicopter fall and hit the bottom with the "biggest explosion you ever heard and then flames like you never seen before".
A series of smaller blasts followed, according to reports.
Hualapai Police chief Francis Bradley said: "It's a very tragic incident.
"Yesterday, we were hampered by severe weather conditions, we had gusts up to 50mph.
"The terrain where the crash occurred ... is extremely rugged."
He told ABC News the tour originated in Boulder City, Nevada, and that a storm was rolling into the area at the time of the crash.
Mr Bradley described the weather conditions as "not normal", but said no flight restrictions were in place.
He told News3LV that darkness and an initial lack of air support hampered the rescue effort.
The three victims who lost their lives in the crash included two brothers, Jason and Stuart Hill.
Jason Hill was a corporate solicitor in Milton Keynes for firm Shoosmiths.
Ms Dobson had worked as a receptionist at Vets4Pets in Worthing, Surrey. On the company's website she wrote: "I love my job and I am hoping to one day fulfil my dream of becoming a Veterinary Nurse!"
The helicopter tour was run by Papillon. The company's website states: "With more than 50 years flying the Grand Canyon and beyond, Papillon is the largest and most experienced helicopter tour operator in the world. "
It further says: "At Papillon Grand Canyon Helicopters, safety is our top priority."
In a statement reported by local news, Papillon Group chief executive Brenda Halvorson said: "It is with extreme sadness we extend our heartfelt sympathy to the families involved in this accident.
"Our top priority is the care and needs of our passengers and our staff."
Federal Aviation Administration spokesman Allen Kenitzer said the Eurocopter EC130 crashed in unknown circumstances and sustained heavy damage.
An investigation will take place.
A Foreign Office spokeswoman said: "We are providing support to the families of six British visitors involved in a helicopter accident at the Grand Canyon on February 10, and we are in close contact with the US emergency services."