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The FBI issued its second highest-priority alert to members of InfraGard - a public-private sector initiative that shares security information.
But the Home Office has insisted there is no increased risk of electronic attacks.
The FBI warned infrastructure owners and operators to be "at a heightened state of alert" and InfraGard co-chairman Phyllis Schneck advised that "increased vigilance would be appropriate for all information systems and services".
The Home Office's Unified Incident Reporting and Alert Scheme (UNIRAS), responsible for dealing with electronic attacks, announced on 12 September that there was no need for special measures.
A statement on the UNIRAS Web site said: "Despite inevitable speculation that yesterday's terrorist attack may be followed by a wave of electronic attacks, there is currently no intelligence to indicate an increased risk of such attacks."
The statement quotes prime minister Tony Blair's message that "business and everyday life can continue as normal", and the police statement that it's "business as usual, reassured by continual review of security measures and contingency plans".
The Home Office told CW360, "This is our current position and there are no plans to change it for the time being."
The National Terrorist Crime Prevention Unit (NTCPU) and the Anti-Terrorist Branch will continually review the situation and advise businesses further if necessary, a spokesman said.
Any new notices can be found on www.uniras.gov.uk