Nextra programme manager, Tracey Cash, said: "This is yet more cost for ISPs on top of the pressure already caused by the Regulation of Investigatory Powers Act. I just wonder if Mr Blunkett has considered the practicalities of implementing these laws."
The company also believes that the government is damaging its vision for an online Britain with the new measures.
Cash explained: "We will try to absorb the extra cost of these laws but we will have no choice but to spread some of the cost to the customer. The government says it wants every business and person online, but this does not help that cause at all and hardly fits into the vision of cost-effective Internet access."
Nextra is hoping that the Internet Service Providers Association (ISPA) will call for urgent talks with the government and produce a White Paper to explain the issues in full.
"We must meet with the government before the end of the year. ISPs have to act as one and put together a plan of attack," said Cash.
The current political climate makes any attempts by ISPs to debate new anti-terrorism laws more difficult.
"ISPs feel they have to be seen to be going along with these measures no matter how much harm they may do to their business," said Cash. "No one wants to look as if they are against the introduction of measures to combat terrorism."