The governor of Basra, Muhammad al-Waili, said on Tuesday the 12 were released after he personally intervened in the matter.
He added that British forces told him that they had received "flawed intelligence about the presence of terrorists in the deputy's home."
There was no official reaction from British troops on the matter.
But the newly elected parliament released a statement shortly after it adjourned on Tuesday. "The assembly holds the leadership of the British forces fully responsible for this operation and demands that the detainees be let go immediately and a formal apology be issued with an explanation of why this happened in the first place."
"We also demand that they compensate the deputy for all material and moral damages suffered," it concluded.
Account of the raid
At the start of the session, which was delayed by three hours, an indignant Mansur al-Tamimi got up from his seat to recount to his colleagues details of the raid on his home in al-Zubayr, south of the port city.
"Last night my family called me saying 40 British vehicles along with two helicopters raided our home.
"They dynamited their way into our home, arrested 11 members of the family including children and even stole money from the house," said a visibly upset al-Tamimi, who is a member of the dominant Shia United Iraqi Alliance bloc.
"I am a member of parliament and I should enjoy some degree of immunity. I am really baffled at this savage treatment by the British."
Witnesses in Zubayr confirmed the account given by Tamimi.
They said the raid, the largest of its kind in the area, occurred at about 3:00am (0000 GMT) and that 12 people were arrested. Those detained included the deputy's brother, Shaikh Salman al-Kanaan al-Tamimi, and another prominent member of the family, Shaikh Muhammad al-Kanaan al-Tamimi.
Basra's notables and tribal chiefs were all gathered at the al-Tamimi residence on Tuesday in a show of solidarity with the family.
Governor al-Waili condemned the incident and warned that "an act like this could plunge the city into discord".