The Open Rights Group, a non-government group that monitors internet-related privacy and legal issues, said it supported the government's decision for a consultation.
"Creating this database would drastically alter the relationship between the citizen and the state, handing national security and law enforcement agencies immense power to invade the private lives of ordinary people," said Becky Hogge, the group's executive director.
At least one senior Microsoft executive doubts how helpful collecting internet communications would be for law enforcement. Hackers have a variety of techniques that could undermine a user's PC and make it appear a victim is involved in a scheme when they're not.
Emails can be spoofed and computers can be infected with malicious software, said Jerry Fishenden, Microsoft's UK National Technology Officer in a blog.
For example, a web feature called 'pre-fetch' lets one website command a person's browser to pull up another website in the background, a feature that speeds browsing.
But pre-fetch works without the knowledge of a user, Fishenden wrote. A blog entry could trigger a bomb-making website to be called up in the background, which would then be logged by the ISP.
"Legitimately you would know nothing about it, but try telling that to someone knocking on your door at four o'clock in the morning waving a printout from the ISP showing you regularly frequent 'known terrorist websites'," Fishenden wrote.