Schools are also receiving adverts from technology firms selling detection equipment, promising to identify texting, e-mails or pupils using mobiles to search the internet.
Among these is Mobysafe, a Gloucestershire company, which is marketing a handheld mobile phone detector to schools.
The firm's owner, David Spurr, says invigilators are faced with communications devices and mobiles which are getting smaller and more powerful.
Tackling cheats who try to use mobile phones is a difficult challenge for examiners.
The jamming of signals is not allowed, because that might interfere with other equipment.
And there have been doubts about the practicality of other tactics, such as sealing rooms with materials which block mobile phone signals.
There have also been suggestions that exam halls could have CCTV cameras installed.
Another approach, tested in Denmark, has been to stop trying to prevent the use of technology in exams and allow pupils to have open access to the internet.
It is not just mobiles which can be misused. All kinds of other types of electronic devices commonly used by teenagers, such as music players, are able to carry useful data or images for an exam.
There are other types of electronics openly sold online as "exam cheat equipment" - including concealed ear-pieces which would allow candidates to receive information in an exam hall.
There are also ear-pieces which can be used wirelessly with concealed digital music players - with the suggestion that lecture notes could be played back to the exam candidate.
These are openly advertised as being of use to students wanting to cheat.
Ofqual's warning to exam candidates specifies a ban on "reading pens and electronic communication or storage devices, including mobile telephones, iPods and MP3/4 players and... any product which can capture a digital image".
In terms of penalties, those candidates who are caught bringing a mobile phone into an exams room - but do not have their phone at their desk - might receive a warning, says the exam watchdog.
But candidates found using a mobile phone during an exam might be disqualified from the unit or the qualification in the current exam series.
Hidden wireless ear-pieces are on sale to listen to music devices
Kathleen Tattersall, Chair of Ofqual, said: "As regulator it is our role to ensure that fair systems are in place and that these are followed correctly.
"We require that awarding bodies report annually on the number of candidates notified as having particular requirements and the number of malpractice incidents reported and investigated.
"These figures provide invaluable information regarding the examination season and allow us to check that the systems put in place to protect learners are followed."
A Department for Children, Schools and Families spokesman said: "Instances of candidate malpractice exams remain extremely rare. The proportion of penalties issued was 0.03% of the total 16 million exams sat by candidates," she said.
"We are absolutely clear that any kind of cheating in exams is unacceptable.
"Ofqual and the awarding bodies take all allegations of cheating extremely seriously to ensure the exam system is not compromised."
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