The warning follows arrests abroad of suspected Islamic militants and the leak of an FBI report that said between five and 15 operations were planned on cities worldwide.
London is considered one of the cities that could be attacked, although senior British police officers and the security services have indicated no evidence has been found of a terrorist plot.
Deputy Assistant Commissioner Alan Fry, the head of the anti-terrorist branch at Scotland Yard, yesterday urged people to be alert.
Mr Fry said yesterday: "There may be groups or individuals who may try to disrupt the celebrations and people should be on their guard against any suspect packages or anyone acting suspiciously.
"Recent arrests in Jordan and the US have heightened the public's awareness of a possible threat from Islamic extremist groups. The public are our eyes and ears and we would encourage them in the run-up to Christmas and the millennium to be vigilant and to contact police if they notice anything suspicious."
Doubts have been expressed that London is likely to be a target because it is used by Islamic organisations as a base.
There will be a huge police operation for the millennium celebrations, with leave cancelled for all Metropolitan police officers.
Last month, police sources revealed Britain was on its highest state of alert since the Omagh bomb last year because of a threat from dissident Irish republican groups.
Scotland Yard urged people to check for unexpected packages when returning from holiday or re-opening businesses and to call 999 if they received an unusual parcel, especially from mainland Europe.Reuse content