Mortars ripped through two stations in the central Ashar district early on Wednesday morning, according to Basra police chief General Muhammad al-Ali.
A British military spokesman, Squadron Leader John Arnold, said the third police station, in the Old City, was destroyed by a car bomb at 07:15 local time. (03:15 GMT)
And two people died when a fourth bomb damaged the police academy and detention centre building in central Basra, according to one governorate councillor, Issam Hazim.
Basra's mayor, Wail Abd al-Hafidh, said around 100 people had been seriously injured and that many children were among the dead and wounded.
The Sadr University Hospital's Dr Ali Ainali confirmed that at least 55 bodies had been brought to the morgue, though staff say there may be more bodies to come.
Three women and two children are among the 25 wounded taken in at another hospital in Basra.
But many more children are believed dead or seriously wounded as two school buses were caught up in the blasts.
Arnold added that although no British soldiers had been injured, they were being prevented from reaching two of the bomb sites because locals were stoning troops.
Only an hour before the attacks, resistance fighters in the Iraqi town of Falluja and US forces began exchanging machine gun fire, mortars and grenades.
Skirmishes were most intense in the town's Golan district at about 06:00 local time.
More than 600 Fallujans have
been killed since 5 April
Occupation forces managed to limit the extent of the fighting by calling in air support.
No more truce
The fighting came hours after US Defence Secretary Donald
Rumsfeld said the truce in Falluja would not continue indefinitely.
He said days of talks involving Iraqi and Sunni Muslim
leaders, Falluja officials and representatives of the US
governing authority in the city did not include Iraqi resistance fighters.
The US marines launched an assault on the city 50km west of Baghdad on 5 April after the killing and mutilation of
four private US security guards the previous week.
Doctors say more than 600 Iraqis have died in fighting in Falluja since.