The arrests in Rome, Milan, Venice, Florence, Naples and other cities on Thursday and Friday were "part of an extraordinary operation that followed the British anti-terrorist operation," Italy's interior ministry said in a statement on Friday.
Twenty-eight people were arrested for violating rules on residence permits and 12 were arrested for property crimes, the statement said, without giving details.
The raids resulted in 114 expulsion orders and found numerous irregularities at call centers, the Internet cafes and the money transfer offices.
More than 4,100 people were also stopped for identification checks, the ministry said.
The raids were made on "Islamic gathering places, including call centers, Internet points and money transfer offices", the ministry said.
In past years, Italian police have made similar sweeps of telephone call centers and money transfer offices in search of people who might be funding or aiding violent Islamic organisations.
The raids of Friday and Thursday come a few days before a top-level meeting on security by intelligence experts takes place in Italy.
The meeting of intelligence and police chiefs had been originally scheduled for Aug. 15 but was moved up a day after the British developments.
Italy also stepped up security at airports and other sites, including those associated with British interests, after the arrests in London, but did not raise its terror alert to the highest level.
Italian anti-terrorism police have also searched the homes of Pakistani immigrants as part of a separate Belgian probe into Pakistanis suspected of financing Lashkar-e-Tayyaba, an south Asian Islamic group linked with Qaeda, the Interior Ministry said Friday. Three people were issued with expulsion orders.