Echoing a warning last week by the head of Britain's domestic spy agency MI5, Reid said authorities were aware of 30 active terrorist plots.
"There are a lot of conspiracies out there," Reid told BBC radio. "These 30 are the ones we think are the most serious of them. They are ongoing, they are working, and they have the potential... some will be nearer preparation than others."
Asked how serious the situation was, Reid said: "It is a very great threat".
MI5 head Eliza Manningham-Buller said last week that her agency was tracking around 1,600 suspects, many of them extremists, most of whom were British-born and linked to al Qaeda in Pakistan.
She also said young British Muslims were being groomed to become suicide bombers.
Asked why suspects were not simply arrested and stopped, Reid said it was difficult to gather sufficient information to constitute evidence strong enough for a prosecution.
"Information is not evidence, this is one of the great problems we have," he said.
"You can have information, you can have suspicion, you can put a case together, but it doesn't naturally constitute evidence, and in this country we have a rule of law which says that in order to try someone you have to have evidence."

Copyright Reuters, 2006