The HH-60G Pave Hawk chopper, based at RAF Lakenheath air base, crashed at a nearby nature reserve in Cley-next-the-Sea, Norfolk, while flying low on a training exercise on Tuesday evening.
Officers from the US Air Force, British Royal Air Force and emergency services worked through the night at the scene of the crash, which cast debris over an area of marshland the size of a football field, Chief Superintendent Bob Scully of Norfolk Police said.
"During the course of the night, police, USAF resources and RAF resources have been conducting a full scene assessment, in difficult terrain," Scully told journalists at the nature reserve, which offers spectacular views of the coast and is popular with bird-watchers.
"That has allowed us to plan for the activities today which will involve further close examination, scene examination, and preserving evidence from the crash site."
The bodies of the four airmen have not yet been removed from the wreckage, he added.
Police were due to pass control of the investigation to the US and British military air investigation branches later on Wednesday, Scully told journalists.
"They will carry out a more technical investigation that may last for some considerable time," he said, adding that it was too early to say what had caused the crash.
The helicopter was carrying live ammunition, and although Scully said this was "not of any great significance", police restricted access to the nature reserve because of bullets scattered over a large area.
Police blocked access to the road running past the crash site, while an area of the marshland was cordoned off.
A second Pave Hawk, which was also training at the time of the accident, was the first vehicle to go to the crashed chopper's assistance, Scully said.
The Pave Hawk is a modified version of the Black Hawk helicopter.
The US 48th Fighter Wing, based at the Lakenheath base, said the names of the four airmen would be released once their families had been informed.
Also known as the Liberty Wing, the 48th is key to US air power in Europe, and is understood to be involved in anti-terrorism operations.
Sue McKnespiey, a shopkeeper who lives near the crash site, said she heard the helicopter flying "very fast and very low" overhead.
"I am used to the sound of helicopters, and this sounded very heavy and very unusual," she said.
"My gut instinct was there was something wrong. We've now heard four people have died and it's just awful."
High winds and torrential rains have battered swathes of Britain in the last few weeks, but the west of the country has borne the brunt of the rough conditions.
Michael Girling, who saw the helicopter shortly before it crashed, described the conditions as "pretty mild, clear, not bad at all".
Pave Hawks are used for combat search and rescue, and are often called upon to retrieve downed aircrew in hostile environments.
During Operation Desert Storm they provided combat search and rescue coverage for coalition forces in Iraq and more than 20 were deployed after Hurricane Katrina in 2005 in support of recovery operations in New Orleans.
Today, Pave Hawks are used in military operations in Afghanistan, Iraq and Libya.
The Norfolk crash comes a month after a police helicopter crashed into a busy pub in Scotland's biggest city Glasgow, killing ten people.
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