In a room at the Old Bailey courthouse in London, six men went on trial this week over an arson attack on a business that was shipping satellite equipment to Ukraine. Down the hall, a separate hearing involved an alleged plot to inflict “serious violence” on Iranian journalists working in Britain. And last month, six Bulgarians were sentenced to prison for being part of a Russian spy ring operating from a guesthouse on England’s east coast.

These disparate cases underscore how Britain has become the locale for a web of foreign espionage operations. For Britain’s top adviser on state threats and terrorism, they offer a stark backdrop to his warning that Russia and Iran are “exploiting divisions in the West” to recruit agents via social media.

The adviser, Jonathan Hall, cannot discuss active criminal cases because of England’s strict reporting laws. But in an interview with The New York Times, he said attempts by Russia and Iran to carry out hostile acts on British soil were creating an “extraordinary” level of threat, albeit one that may be harder for the public to grasp than that from terrorism.

“Terrorism is something that gets public attention,” Mr. Hall said, partly because of the “death and destruction and mayhem” caused by attacks. State threats, he said, were “much harder to conceptualize” for the public.

Mr. Hall’s warnings, and those of other senior British officials, stand in sharp contrast to the United States, where President Trump has said little about the efforts of Russia and Iran to destabilize American society, preferring instead to focus on diplomatic overtures to the two countries on issues like the war in Ukraine and Tehran’s nuclear program.

Mr. Trump’s approach comes even as American authorities have tracked what they believe to be Iranian plots to assassinate the president — allegations that Iran denies — and former intelligence officials have spoken of Russian agents in Mexico who have tried to encourage illegal migration into the United States.