Decontamination teams have been called into action
Chief Superintendent Kevin Morris, chairman of the Police Superintendents' Association, told the BBC: "People could see a prison sentence if they undertake a hoax of this nature."
Emergency services went on alert again on Wednesday morning after suspect packages leaking white powder were found by postal workers in Hatfield and Chelmsford.
GPs and front-line health staff are to be given additional information about clinical and laboratory procedures on "biological matters", later on Wednesday.
Downing Street says this is complementary to guidance sent out last week.
'Be alert'
Chief Superintendent Morris said: "If we are going to get a lot of well-intentioned alerts, we will deal with those, but it's going to take a lot of time, and divert us from perhaps more important things.
"If they are hoaxers, then we will pursue them through to the courts."
But he said anyone receiving a suspicious package in the post should take it seriously and put it somewhere safe, seal the room, stop anyone going in and call a police station for advice.
Prime Minister Tony Blair's official spokesman urged the public to "retain a sense of perspective".
He called on people to remain vigilant but added that there was "no evidence of any specific threat to the UK".
"We understand why people are concerned when they see events in the US," the spokesman continued.
"People should not be unduly concerned - but it is important for the government to make appropriate contingency and public health planning arrangement, which is what we are doing."
Two incidents in London and one in Liverpool on Tuesday all proved to be harmless.
Police gave the all-clear at Liverpool's Royal Mail sorting office, which was evacuated after a suspect powder - later found to be sand - was discovered at the site.
A suspect package which saw the London Stock Exchange evacuated was later found not to contain any trace of anthrax.
Buildings evacuated
Canterbury Cathedral was evacuated on Sunday after a man was seen dropping white powder in one of the chapels. The powder was found to be harmless, but the man slipped away unchallenged.
Emergency services were called to the Royal Mail sorting office in Hatfield on Wednesday after a suspect package was found by workers there in the early hours of the morning.
Specialist consultants from the Metropolitan Police have been called in to check and identify the contents of the package.
Police said there were no injuries and there was no cause for alarm, although six staff are undergoing a cleansing procedure as a precaution.
In Essex, the sorting of overnight mail was disrupted after a suspect package prompted the evacuation of over 700 Royal Mail employees from the sorting office at Boreham, near Chelmsford.
Police and fire crews were called to the scene and two hours afterwards declared the area safe.
In London police were called to the Middle East Broadcasting Centre after a suspicious letter containing white powder was sent to the Head of News.
There were also alerts at postal sorting offices in Preston and Bradford.
And the third floor of the 20-storey Driver and Vehicle Licensing Agency headquarters in Swansea was evacuated and sealed off after a suspect package was spotted in the post room.
There was also a false alarm at Millbank in London - where the BBC has studios - at about 2035BST on Tuesday.