It is the first time Ken McCallum, the security service’s director general, addressed the conflict.
The “monstrous attacks” on Israel could increase the risk of terror atrocities in the UK and raised concerns about the threat from Iran, he said.
Mr McCallum said the regime already posed a “particularly intensive” threat but may now “move into new directions”.
“We have obviously been concerned about Iran’s behaviour in the UK for a long time,” he said.
“In particular, the last 18 months or so have been a particularly intensive phase of Iran-generated threat on UK soil.
“Plainly, events in the Middle East sharpen the possibility that Iran might decide to move into new directions.
“I wouldn’t rule out the possibility that could include the UK, but we are already operating at a high level of Iran-generated threat.
“For the most part, the activity we’ve seen backed by Iran in the UK for the last 18 months or so has been targeted at the regime’s own internal enemies, dissidents, Farsi media organisations. Not exclusively, but predominantly.
“Clearly, one of the things on our minds is, might the Iranian targeting intent shift in response to events elsewhere.”
Mr McCallum also warned businesses to protect themselves against Chinese hackers amid a “sharp rise” in aggressive action by foreign powers.
Those involved in new technology such as artificial intelligence, quantum computing and synthetic biology are being told to take action to protect their intellectual property.
As well as cyber security, companies are being warned to be aware of new investors if they are not sure where their money has come from.
Entrepreneurs can end up signing contracts that see their intellectual property taken offshore and lost for good.
Intelligence services across the Five Eyes alliance – the UK, US, Canada, Australia and New Zealand – are all issuing similar advice, particularly to start-up businesses in emerging technologies.
“Across all five of our countries we are seeing a sharp rise in aggressive attempts by other states to steal competitive advantage," Mr McCallum said.
“This contest is particularly acute on emerging technologies. States which lead the way in areas like artificial intelligence, quantum computing and synthetic biology will have the power to shape all our futures.
“We all need to be aware, and respond, before it’s too late.”
Mr McCallum on Tuesday appeared onstage with the other heads of the Five Eyes intelligence services in public for the first time, at an event hosted by the Hoover Institution at Stanford University and the FBI.
“There is no greater threat to innovation than the Chinese government," FBI director Christopher Wray said at a panel to open the summit.
"And it is a measure of how seriously the five of us and our services take that threat that we have chosen to come together to try to highlight that, raise awareness, raise resilience and work closely with the private sector to try to build better protection for innovation, especially in a place like northern California but really across all five of our countries."
Guidance has been drawn up by the protective security arm of MI5 and part of GCHQ, which will be made available for businesses in the UK.
It covers areas including investments, supply chains, travel, IT networks and cloud computing.
While there is also concern about countries including Russia and Iran, the main warnings are focused on China.
The number of investigations by the UK intelligence service into Chinese activity of concern rose seven times between 2018 and 2022.
Last summer in a rare public appearance with Mr Wray, Mr McCallum revealed that the UK had shared intelligence about Chinese cyber threats with 37 countries in the past year, and disrupted a “sophisticated threat” against aerospace companies.
Examples of interference by the Chinese government included a British aviation expert who was paid for technical information on military aircraft by a company that turned out to be a front for China’s intelligence service.
In another case, engineering firm Smith’s Harlow was forced into administration in 2020 after it entered into a deal with a Chinese company that abandoned the partnership after the UK firm company shared vital technology.
There are also investigations into possible Chinese influence in the UK parliament.
In September it emerged that a parliamentary researcher had been arrested on suspicion of spying for China.
And in a separate case in 2022, MI5 warned MPs that a suspected Chinese spy named Christine Lee had allegedly engaged in “political interference activities” on behalf of China’s ruling communist regime.