The group, which represents MPs, peers and IT directors, is calling for the Government to provide the police and businesses with the powers they need to fight computer crime.
"While hacking, pornography and other Internet crimes make headlines, real damage is being done by electronically-assisted conventional crime," Eurim said in a policy paper.
The global cost of e-crime is about $1tn, according to US estimates and the UK economy will have to bear a significant share of this, Eurim said.
But the group argues that it is difficult to take action in the UK against electronic criminals. "If a supermarket is burned down the police investigate and the judge will be severe. If an e-business is similarly destroyed, the police rarely afford it the same attention and experience," it said.
The paper calls for co-operation between law enforcement agencies, IT suppliers and IT users to share experience on prevention, deterrence and detection and to develop new legislative approaches.
The lobby group is pressing for the Law Commission to review existing UK legislation to ensure that e-crimes can be prosecuted effectively.
Other recommendations include: the development of a national strategy on e-crime in conjunction with businesses, consumer and civil liberties groups and government; and greater corporation between businesses and the National High Tech Crime Unit.