Scotland Yard has charged three men under the Terrorism Act - but no specific plot or weapons have been mentioned.
Detectives have declined to comment on reports in a Sunday newspaper that the Tube network had been the target.
Deputy Prime Minister John Prescott also played down the significance of the arrests, saying they had "excited the press".
But he said the general terrorist threat remained high and warned the public to remain vigilant against any possible attack.
Mr Prescott told the BBC: "As the prime minister reminds us, we get an awful lot of intelligence which we have to make judgements about.
"In this case it does not appear there is any evidence whatsoever there was going to be a gas attack or use of bombs regarding the three people who have been arrested."
The Sunday Times speculated the men had planned to release cyanide gas on the London Underground.
'Strong alert'
But police said no cyanide or noxious gas had been found on them when they were arrested on 9 November.
A Home Office spokesman said a public warning would be made "without hesitation" if the government or police thought it necessary.
Mr Prescott added: "If it is a direct threat that we know and can prove then the public will know about it.
"But at the same time we keep up a very strong alert. Our forces, police, intelligence services are working flat out to make sure we have the highest possible safety for our citizens."
His Conservative counterpart, David Davis, told BBC News: "The public should be told the general level of risk.
"How much they should know about the detail is entirely a function of what is best for the safety of the public."
The men, who are of North African origin, were charged under Section 57 of the Terrorism Act 2000 for the possession of articles for the preparation, instigation and commission of terrorism acts.
The trio are Rabah Chekat-Bais, 21, Rabah Kadris, in his mid-30s, and Karim Kadouri, 33, all of no fixed abode.
They appeared in court last week and were remanded in custody to appear before magistrates again on Monday.
Prime Minister Tony Blair, who this week warned the public to be vigilant for any terrorist attacks, has been kept informed by police.
Last week, there was confusion over the extent of Home Office fears over a chemical attack on the UK.
A warning of a possible chemical or nuclear terrorist attack on the UK using a "dirty bomb" or poison gas, was quickly withdrawn and replaced with more general advice.