Both AP and Reuters are reporting that detectives from London, together with local officers, searched four properties in West Yorkshire under warrants issued under the Terrorism Act and were examining a fifth.
The searches were part of a pre-planned intelligence-led operation, a spokeswoman said, but there have been have been no arrests at this stage.
"The searches are in connection with the terrorist attacks in London on July 7," she added.
An anti-terrorist police spokeswoman said the searches were thought to be "significant".
Tuesday's operation was the first reported swoop in what police describe as the biggest crime scene investigation in English history.