"We are going into crisis mode", a source at Whitehall told the Sky News broadcaster.
The current level of crisis is still low, but it could go up if the situation becomes aggravated, the media added.
Another source told the media that the number of additional Foreign Office workers focused on Iran had increased fivefold.
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The decision came a year after the United States pulled out of the deal and reinstated wide-ranging sanctions on Tehran, including restrictions against companies and financial institutions of countries that do business with the Islamic republic. Iranian President Hassan Rouhani has given European countries 60 days to organise talks on the matter.