Rt Revd Richard Chartres made the comparison in a sermon during the Maundy Thursday Chrism Mass at St Paul's Cathedral.
Mr Chartres was referring to the government's instruction for schools to teach "British values" in order to stop extremism, after widespread claims radical Islamic ideology was being taught and encouraged at some schools in Birmingham.
The claims prompted response from the government in what is now known as the Operation Trojan Horse scandal.
His use of the term 'Big Brother' is a reference to George Orwell's famous novel 1984, where Big Brother is the leader of an authoritarian government which constantly surveys the masses and manipulates their thoughts and factual history in order to stay in power.
Ofsted's list of 'British values':
Democracy.
The rule of law.
Individual liberty.
Mutual respect for and tolerance of those with different faiths and beliefs, and for those without faith.
Rt Revd Chartres expressed concern that attempts to teach British values was leading to the removal of all religion from schools, which he argued is not only negative in and of itself, but would also ironically help to fuel extremism rather than prevent it.
He said in his message: "With the atrocities in Brussels and Paris very much in our minds it should be obvious that you cannot exorcise the Satanic by creating a spiritual vacuum.
"The nakedness of the land has recently been illuminated by the attempt to enlist schools in the communication of 'British values' as a way of combating 'extremism'.
"Merely invoking universal abstractions like tolerance, fairness and civility cannot generate one iota of the energy needed to build a community and transform individual lives.
"Any education to equip young people to face the promise and peril of life in the 21st century must include a commitment to religious literacy, ethical clarity and spiritual awareness.
"The business of the State is to ensure that the living traditions in our pluralist society have space to flourish without the State itself being drawn into the role of an ideologically driven Big Brother, profligate with ever more detailed regulation."
