Britain's enemies are "rubbing their hands with glee" over whistleblower Edward Snowden's NSA leaks, the MI6 chief said.
GCHQ have launched an online code breaking competition to find people capable of joining the Government's national cyber security teams.
The Foreign Secretary said British intelligence would never use its partnership with the United States to get around UK laws.
GCHQ boss Sir Iain Lobban listed current key cyber threats: industrial espionage, terrorists, hacktivists, highly-sophisticated criminal actors, non-state actors, and "engagement by some states as an over-the-horizon means of disruption."
MI5 has disrupted 34 terrorist plots "at all sizes and stages" since the 7/7 bombings in London in 2005, Andrew Parker told the committee.
"The vast majority come from people who live here."
"Terrorist tourism" is growing, especially to places like Syria, MI5's Andrew Parker has told the committee.
Britons in their "low hundreds" have gone to Syria to align with Al-Qaeda-affiliated groups operating there, he said.
Sir John Sawers told the committee that if any of Britain's security agencies were unsure about a decision, "we would wake up the Foreign Secretary in the middle of the night".
"With the benefit of hindsight we were not configured in 2001 for the scale of terrorism this country faced after 9/11," Sir John Sawers told the committee.
"It took us some time to adapt to the scale of the threat that we face."
MI5 boss Andrew Parker said all three security agency directors are in discussions about the number of US security staff who appear to have access to British secrets, as NSA whistleblower Edward Snowden did.
GCHQ director Sir Iain Lobban told the committee that the internet gives terrorists "a myriad of ways to work covertly" as well as platforms for fundraising and recruiting.
Asked why intelligence agencies did not foresee the end of the Cold War, 9/11 or the Arab Spring, Sir John Sawers said: "We are not crystal ball gazers, we are intelligence agencies."
"We acquire the secrets that other countries do not want us to know. We are not all-knowing specialists in what is going to happen next month or next year."
"There are a very wide range of threats that we face," MI6's Sir John Sawers has told the committee. "The biggest is terrorism."
"There are also states out there that are trying to do us harm," he said.
Members of public can watch the three security agency directors appear before MPs on the Parliament website.
The feed is subject to a two minute delay.