British military commanders suspect that groups with connections to Iraq's Shia cleric Muqtada al-Sadr have been aided by Iran in carrying out the attacks.
Sources in al-Sadr's Basra office said most of those arrested were al-Sadr supporters.
The raids came hours after British Prime Minister Tony Blair said London suspected Iran and Lebanon's Hizb Allah might be supplying technology and explosives to Shia Muslim groups operating in Iraq.
But the prime minister said he had no proof.
Hizb Allah and Iran deny the accusations.
British military spokesman Major Steven Melbourne in Basra said: "We had an operation last night in Basra and 12 people were arrested. The investigation is ongoing and we cannot give any details about the people who were detained.
"There have been a lot of attacks against multi-national forces in recent weeks and there were certain individuals that we needed to question and about whom we had good intelligence."
British and US forces have been repeatedly attacked in recent months by roadside bombs packed with "shaped charges", which are more deadly than conventional roadside bombs.
Observers said those arrested
were supporters of al-Sadr
Six British troops have been killed since July in attacks that appeared to be the work of the more powerful bombs.
Blair, speaking during a news conference in London with Iraqi President Jalal Talabani on Thursday, said: "What is clear is that there have been new explosive devices used not just against British forces but elsewhere in Iraq. The particular nature of those devices leads us either to Iranian elements or to Hizb Allah ... However, we cannot be certain of this at the present time."
Sources in al-Sadr's office in Basra said those detained included several lieutenants in Basra's interior affairs department, which is part of the interior ministry, and an official with the local electricity authority.
"They are mostly al-Sadr people," one of the sources said.
Police search the rubble at the
police station hit by the British
He said some of the suspects were seized from the police building that British forces attacked late last month to free two undercover soldiers who had been detained by Iraqi police.
The British military spokesman would not confirm that.
The arrests run the risk of increasing tensions between the 8500 British troops serving in Iraq and the local population.
After the detention of the two British soldiers last month, angry crowds of young men attacked British military vehicles with petrol bombs and rocks, forcing a unit to pull back.
The sources in al-Sadr's office said the arrests took place late on Thursday, shortly after the men had broken fast on the second day of Ramadan, the Muslim holy month, in what could be seen as a slight and provoke more anger.
The military spokesman in Basra would not say exactly when the arrests took place, however, saying only that they had been conducted peacefully, with no shots fired, and that more details would be made available shortly.