Security sources said they all have links to Islamist groups – and are believed to be backed by Iran.
The six suspected terrorists are understood to have arrived in the UK illegally from northern France weeks ago, after travelling across Europe from Syria.
MI6 spies stationed near the Syrian capital Damascus reportedly uncovered an Iranian-backed plot against Britain before Hamas’s massacre in Israel last month.
The cell’s mission is not thought to be linked to the ongoing war in Gaza.
An intelligence source told the Express: “The information indicates that these people are terrorists planning to attack government buildings in England, Scotland and Wales.
“Although they arrived without identification, we believe all are now in possession of false documents.
“They plan to commit an act which embarrasses the Government.
“This could mean damaging a building or even a close-proximity cyber attack, though we do not anticipate this is a mass-casualty event.”
Spooks are tracking the movements of three of the fugitives – but the other three have reportedly disappeared with the help of fake ID documents.
The known suspects are reportedly being kept under surveillance in the hope they will lead security services to the other members of the alleged terror cell.
Anti-terror chiefs are also understood to believe that they could face a lengthy legal battle if they try to remove the suspects.
Around 25 terror suspects have reportedly entered the UK illegally this year.