Soldiers cordoned off the area around the crash site
The scenes in Basra
Iraqi police claimed five local people were shot dead in the unrest, although they did not know who fired the shots.
The city has been placed under a night-time curfew to defuse tensions.
Earlier Basra police said the aircraft crashed into a house after being hit by a rocket, but British ministers said the cause of the crash was unclear.
Defence Secretary Des Browne offered his sympathies to the families of the servicemen who died.
BBC correspondents in Iraq say the events have opened a new chapter for British forces in the area - and it will be increasingly difficult for them to control Basra's streets.
Basra police said four people were killed in subsequent clashes
According to police in the city, two children were among those killed and a further 19 people were wounded during the disturbances after the helicopter came down.
Gen John Cooper, commander of the British forces in Iraq, said troops did not fire directly into the crowds but fired live rounds at targets threatening them.
Major Sebastian Muntz, in Basra, could not confirm claims that people had died in the disturbances.
He said the curfew, in force from 2000 to 0600 local time, was doing its job and the situation near the crash site was calm.
Mr Browne, who has only been in the job since Friday, said he was "deeply saddened" by news of the crash, but warned against speculation over what had caused the incident.
"The situation on the ground is still developing and facts are still coming in. We must be careful to allow those investigating the incident to do their job."
In other developments:
A suicide bomber wearing an Iraqi army uniform entered an Iraqi army base in Tikrit and detonated an explosives belt, killing three army officers
Two Iraqi policemen were injured by a roadside bomb in the northern city of Mosul
In Baghdad, two children were killed and a woman injured when a mortar landed on their house in the north of the city
Crowds of Iraqis cheered and celebrated near the site of the helicopter crash as the wreckage burned.
Iraqi youths threw stones at British troops after the crash
The BBC's Andrew North said it was a sign of a "dramatic change in attitude" towards the British presence in southern Iraq.
As the troops moved in to secure the area, they came under a hail of stones and several armoured vehicles were set alight by petrol bombs.
Exchanges of gunfire took place but it was not clear where from, and it is thought the troops may have been the target of mortar shells that came down among the crowds of Iraqis.
Maj Muntz said although the scenes in the city had been "horrible", the general situation had been improving recently.
But our correspondents said Saturday's events made it clear that the number of people who wanted the British out was rising.
If confirmed, it would be the first time a British military helicopter had been shot down in the area.
The Liberal Democrats described it as an "appalling incident" and called for a "clear exit strategy" for British forces from the area.
Shadow defence minister Liam Fox said: "This incident raises a number of questions about the state of our airmen, which I am keen to pursue with the new secretary of state as soon as possible."
The MoD said it was not the right time to be discussing strategy, saying their efforts were concentrated on dealing with the situation on the ground.
More than 100 British service personnel have been killed in Iraq in total.
A hotline has been set up for families seeking information: 08457 800 900.
A British military helicopter crashed in Basra on Saturday killing four crew members. Local Iraqis filled the surrounding streets celebrating the crash before a clash occurred with British troops upon their arrival.

"We can confirm it was a British military helicopter that has crashed and an investigation is ongoing," a British military spokesman in London said.

An AFP reporter on the scene heard from a local policeman that the helicopter was hit by a rocket fired by local militia.

According to Basra police spokesman Lieut. Colonel Kareem al-Zaidi, "a multinational forces helicopter was hit by a rocket and went down on houses in central Basra". He also added that fire-fighters later found the four British crew members charred in the wreckage and that no causalities on the ground resulted from the impact.

Earlier, an AFP journalist sighted the downed British military helicopter and reported he saw two burnt crew members after the impact which caused the helicopter to burst into flames.

After the crash, it is reported that hundreds of people from the local area, many of them youths, celebrated the helicopter's downing in the streets surrounding the crash.

On the arrival of British troops at the scene, including two tanks and one land rover,  the crowd allegedly attacked the British forces with rocks, debris and petrol bombs.

A British spokeswoman, Capt. Kelly Goodall, said British soldiers who responded came "under attack by a variety of weapons, including small arms fire, petrol bombs, as well as blast bombs and stone."

British soldiers used foam to extinguish their vehicles, escaping uninjured.

Members of the crowd allegedly shouted slogans such as "victory for the Mehdi Army!" and "we are all soldiers of al-Sayed" in support of local militants lead by Shi'ite Muslim cleric Moqtada al-Sadr.

During the conflict, An AFP photographer was shot and wounded in the leg by a rubber-coated bullet. Contrary to reports from the British defence department, the journalist said that British soldiers raised their rifles and shot one man dead and also later shot the driver of a car in a local street dead.

As conflict was escalated, British and Shi'ite gunmen exchanged fire which resulted in the addition deaths of four Iraqis including two children. An estimated 30 civilians were reportedly injured in the melee.

An Iraqi policeman in Basra said the helicopter was downed by a rocket and said four Iraqi civilians, including two children, were killed and another 19 wounded in the fighting.

Military forces later cordoned off the scene and imposed a curfew on the surrounding area in Basra.