On December 12, six people from London, Derby and Burton upon Trent were arrested on suspicion of preparing a terrorist attack.
The alleged targets were one or more shopping centers in the run-up to Christmas, The Independent reported, citing security sources.
On Thursday, two of the men from the Derby area were released without charge, while the other four people remain in custody.
The security operations, according to senior sources, were carried out in direct response to information about terrorist threats linked to Daesh. During the raid, officers reportedly recovered materials which could be used for making bombs.
The UK reports come several days after a truck rammed into the crowd at the Berlin Christmas market on the Breitscheidplatz square on Monday, killing 12 people and injuring almost 50 others.
Daesh, which occupies vast tracts of Iraq and Syria and is outlawed in many countries including Russia, has gained much notoriety for conducting suicide bombings and other attacks worldwide and recruiting young people via social media.