MANCHESTER, England — British officials expressed confidence on Friday that they had rounded up the bulk of the Manchester bomber’s associates, and that their efforts to avert a follow-up attack appeared to be succeeding.

“We’ve got hold of a large part of the network behind Manchester bombing,” said Mark Rowley, the top counterterrorism official for the Metropolitan Police in London.

Eight men, ages 18 to 38, were in custody, and searches were still taking place at 12 locations in the Manchester area, the city’s top police official, Chief Constable Ian Hopkins, said at a news conference. “There has been enormous progress with the investigation, but there’s still an awful lot of work to do,” he said.

The latest raids occurred Friday morning at a barbershop in the Moss Side neighborhood and at a pizza restaurant in St. Helens, a town about 20 miles west of Manchester.