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Candidates in the general election have been asked to look through their emails for signs that they have been targeted by a phishing attack.
The list of potential targets includes recent MPs.
The National Cyber Security Centre (NCSC), which is part of GCHQ, disclosed the request in a document released early on 16 May.
The BBC understands that the number of victims is currently understood to be in single figures.
Candidates have been asked to look for suspicious emails received after Jan 2017.
The NCSC declined to say if any data had been taken.
A report in the Financial Times said it was "likely" that the phishing campaign had been orchestrated by a state.
In a document titled Phishing: guidance for political parties and their staff, the centre says it has "become aware of phishing attacks to gain access to the online accounts of individuals that were MPs before dissolution of Parliament" and "other staff who work in political parties".
The NCSC said the attacks were likely to continue "and may be sent to parliamentary email addresses, prospective parliamentary candidates, and party staff".
The BBC understands that so far victims' personal emails have been affected but no successful phishing attempts have been made via parliamentary email addresses.
It is believed that the NCSC has contacted the Electoral Commission about the threat and that the commission will help to alert candidates.
The centre said that potential victims should look out for "unexpected requests to reset your password for online or social media accounts (such as Apple, Google, Microsoft, Facebook or Twitter)".
"Or you might have been asked to approve changes to your account that you've not requested."
The NCSC did not say whether it knew who was behind the phishing campaign.
The warnings to political parties come as cyber-security officials brace themselves for some kind of incident during the elections.
No-one can be sure that anything will take place, but the experience of the US and more recently France has led them to believe that some kind of theft and then dump of information is possible.
In both those cases, a Russian hand is suspected.
Intelligence agencies have historically kept their distance from the communication of politicians due to the doctrine that says MPs should not be monitored.
But parties and politicians themselves have been asking for advice and guidance in recent months amid growing concerns.
Concern about elections being targeted by hackers has been running high, following the attack on the Democratic National Committee during the US presidential election.
US authorities attributed that incident to Russia and said that a significant component of the attack involved phishing.
More recently, the electoral campaign of President Emmanuel Macron in France was targeted by a similar campaign.
The NCSC has said the UK has "systems in place to defend against electoral fraud at all levels and [we] have seen no successful cyber-intervention in UK democratic processes".
The BBC understands that since last month, the NCSC has delivered cyber-security seminars to the UK's political parties, with the aim of helping them reduce the risk of succumbing to an attack.
Advice has also been offered to local authorities and the electoral commission.
