By Susannah Price BBC correspondent in Baghdad

The uniformed soldiers were in a four-wheel-drive vehicle, travelling with a military Land Rover through the city centre when they came under fire.

Eyewitnesses said that gunmen in a pickup truck opened fire on the soldiers, who shot back. The attackers then threw a grenade at the vehicle.

"I heard an explosion and I saw a car carrying three people hitting the pavement and it was followed by another car," said one eye witness.

Particularly worrying

The BBC Arabic Service reporter Issam Alainachi was on the scene within 10 minutes.

British troops have stepped up security since the attack

"When I got there I saw two British soldiers' bodies and the people there were still waiting for ambulances," he said.

"People told me that three had been killed in the firing."

This attack will be particularly worrying for the British forces in Basra, Iraq's second largest city, who had been trying hard to win over the local people.

They had carried out patrols on foot, sometimes without body armour and helmets, although they often risked being stoned by gangs of children.

'Potential threat'

However, they had recently been taking more precautions.

"For the last couple of weeks, British soldiers have been wearing body armour on the ground because it felt the potential threat was sufficient to warrant that," said Major Ian Poole, British Army spokesman in Basra.

"It is also important to try to reduce the physical barriers between ourselves and the local community and it is a case of trying to strike a balance here."

Before this latest attack seven British personnel had been killed in operations since the beginning of May.

Six members of the Royal Military Police were killed by a mob angered by controversial house searches in a village in the south.

Explosive device

In early August there were riots in Basra protesting against the frequent electricity cuts and serious fuel shortages during the intense summer heat.

The Shia religious leaders have told people they should not kill anyone - including American or British soldiers BBC reporter Issam Alainachi

A few days later a soldier was killed and two others wounded in the city, when an explosive device was set off next to the military ambulance they were travelling in.

This is in stark contrast to the Americans, who have faced a continuing guerrilla campaign and mounting casualties, particularly in the so-called Sunni triangle - the area north and west of Baghdad where support for Saddam Hussein was strongest as well as in Baghdad itself.

Basra on the other hand is a predominantly Shia Muslim area, scene of an uprising at the end of the Gulf War, which was brutally suppressed by Saddam Hussein.

"The Shia religious leaders have told people they should not kill anyone - including American or British soldiers," said Mr Alainachi of the BBC's Arabic Service.

"The people do not seem to have any major problems with the British soldiers."

Daily operations

The British Army has started an investigation into the latest deaths.

It will be working with the Iraqi police and Basra officials.

One of the key questions will be whether this was carried out by those from Basra - or if the attackers came from outside the city, or even outside Iraq.