The head of MI5, Andrew Parker, has called for new powers to help fight Islamist extremism, warning of a dangerous imbalance between increasing numbers of terrorist plots against the UK and a drop in the capabilities of intelligence services to snoop on communications.

Parker described the Paris attack as “a terrible reminder of the intentions of those who wish us harm” and said he had spoken to his French counterparts to offer help.

Speaking to an invited audience at MI5 headquarters, he said the threat level to Britain had worsened and Islamist extremist groups in Syria and Iraq were directly trying to orchestrate attacks on the UK. An attack on the UK was “highly likely” and MI5 could not give a guarantee it would be able to stop it, he said.

“Strikingly, working with our partners, we have stopped three UK terrorist plots in recent months alone,” he said. “Deaths would certainly have resulted otherwise. Although we and our partners try our utmost, we know that we cannot hope to stop everything.”

Britain had increased security checks at the French border, including extra vehicle searches, in light of the Paris terrorist attack to make sure the suspects do not enter the country, Downing Street said .

The UK faces many of the same threats as France and the rest of Europe from al-Qaida, from extremist groups in Syria and Iraq and from elsewhere in the Middle East, Asia and North Africa.Parker claimed Islamic State was “trying to direct terrorist attacks in the UK and elsewhere from Syria, using violent extremists here as their instruments”. It was also “seeking through propaganda to provoke individuals in the UK to carry out violent attacks here”.

About 50% of MI5’s work is now devoted to counter-terrorism. Parker said: “My sharpest concern as director general of MI5 is the growing gap between the increasingly challenging threat and the decreasing availability of capabilities to address it.”

Almost all of MI5’s top-priority UK counter-terrorism investigations had used intercept capabilities in some form to identify, understand and disrupt plots, he said. “So if we lose that ability, if parts of the radar go dark and terrorists are confident that they are beyond the reach of MI5 and GCHQ, acting with proper legal warrant, then our ability to keep the country safe is also reduced.”

The intelligence agencies in the UK and the US claim that the Snowden revelations in 2013 about the scale of bulk data collection have undermined their capabilities. Parker said: “We all value our privacy – and none of us want it intruded upon improperly or unnecessarily. But I don’t want a situation where that privacy is so absolute and sacrosanct that terrorists and others who mean us harm can confidently operate from behind those walls without fear of detection.

“If we are to do our job, MI5 will continue to need to be able to penetrate their communications as we have always done. That means having the right tools, legal powers and the assistance of companies which hold relevant data. Currently, this picture is patchy.”