Justice Lowell Goddard, who is leading the probe, also said councils in Lambeth, Nottinghamshire and Rochdale will be examined.
Speaking in central London the judge set out 12 different areas which will come under scrutiny.
The probe was set up last year following claims of a high-level cover up of abuse and has been beset by delays following the resignations of two previous chairwomen.
It will be Britain’s largest-ever public inquiry and is expected to take up to five years and cost tens of millions of pounds.
Justice Goddard said: “The investigation will focus on high-profile allegations of child sexual abuse involving current or former members of parliament, senior civil servants, government advisers and members of intelligence and security agencies.
“It will consider allegations of cover up and conspiracy and review the adequacy of law enforcement responses to these allegations.”
The probe will also focus on child sexual abuse in the Roman Catholic and Anglican churches, she said.
She added: “There is no doubt that the task we have set ourselves is ambitious. To run 12 investigations in parallel represents an organisational challenge that is unprecedented in a public inquiry in the United Kingdom.
“We are determined to succeed and expect full co-operation of all institutions and individuals who can assist us in our work.”