Warnings from the new director of GCHQ, the UK’s eavesdropping agency, that US technology companies are not doing enough to prevent social networks becoming “the command-and-control networks of choice” for terrorists are reactionary and inflammatory, according to Martha Lane Fox.

The tech pioneer, who founded Lastminute.com and in 2010 became the youngest woman to sit as a cross-bench peer in the House of Lords, described Robert Hannigan’s comments as the “most fabulous PR job for day one” of his new job.

Speaking on BBC Radio 4’s Today programme, Lane Fox, who previously worked as the government’s tsar for digital inclusion, said tech firms had an obligation to work with government, but there were “clear” legal routes to enable governments to extract information from then if necessary.

“If you have reasonable suspicion, there is a court process by which you can demand all sorts of things,” she said. “The security services’ reach is enormous.”

In an opinion piece written for the Financial Times, Hannigan argued that a new generation of freely available technology had helped groups such as Islamic State (Isis) hide from the security services and accused tech firms of being “in denial”.

GCHQ needed to enter into the debate about privacy, he added. “I think we have a good story to tell. We need to show how we are accountable for the data we use to protect people, just as the private sector is increasingly under pressure to show how it filters and sells its customers’ data,” he wrote.

“GCHQ is happy to be part of a mature debate on privacy in the digital age. But privacy has never been an absolute right and the debate about this should not become a reason for postponing urgent and difficult decisions.”

Lane Fox said of his comments: “This reactionary and slightly inflammatory comment doesn’t help the overall picture when we should be having a considered debate.” She added that previous figures had warned about new technologies being used by criminals, such as the telephone by gangsters, adding “perhaps it was ever thus”.

Lane Fox said in the digital era the boundaries between one’s personal space and digital space had been blurred and the public were right to demand that both remained private.

“I would not want GCHQ to come and rummage in my front room and that is how I feel about whatever device I am using,” she said. “We have to have a debate about how we handle of the complexities of this brave new world.”