The arrests came after an air show
The 11 men and one woman, all with an organisation called Touchdown Tours, are being held in a jail in Kalamata in the southern Peloponnese.
They have denied the charges, saying they are simply aviation enthusiasts on a plane-spotting holiday.
They were arrested on Thursday after attending a public event to mark a Greek air force holiday at a nearby military airfield.
Diplomats have said they are being well treated.
The Britons have been allowed to speak to relatives, and the British Consul will attend the court hearing.
Regular trips
Paul Coppin, from Mildenhall, Suffolk, runs the firm and is one of the people being held in Greece.
Others detained include Peter Norris, 52, of Uxbridge, west London, Mick Keane and Steve Rush, the Foreign Office confirmed.
Two Dutch citizens were also members of the group.
Touchdown Tours organises regular overseas trips for military aviation enthusiasts, including a similar trip to Greece last year, and its website admits they can become "a bit riotous".
This year's week-long excursion cost £650 and the group had been due to return to the UK on Sunday.
Puzzled
Puzzled British diplomats have been talking to the detainees, to try to establish exactly what happened.
Officials say it looks as if they were a harmless group of respectable plane-spotters, but there is concern that the Greeks could take a more serious view.
The initial charge was taking photographs in a restricted area, but worryingly that was later changed to a more serious charge of spying.
Written invitation
British diplomats say they understand the group did have a written invitation to attend the air show, but one which would have included a strict no-photography clause.
The group have denied taking any photographs and say they were using only binoculars.
However, diplomats are worried about a report that they had already been cautioned in Athens for a similar offence and about a claim from Greek police sources that notebooks were seized containing details of several military airports.
A lawyer for the group has expressed confidence that it is all a misunderstanding, and that Greek British relations are not about to be troubled by a major spying scandal.
Aircraft logged
Touchdown Tours' website says that last year a group visited 18 bases in five days, logging more than 700 Greek military aircraft at bases including Kalamata.
But it cautions: "I would warn that spotting in Greece is still not particularly liked by the authorities and without our contacts at the Greek Ministry of Defence, which helped on a number of occasions, the trip might have been a little longer than anticipated!"
The tours, in which the group travel around by minibus, involve visits to plane wreckage, operational airfields and bases.
The website adds: "Apart from the spotting we do also aim to have some fun on the trips, and a good sense of humour does help.
"There are usually a number of occasions on each tour when an evening of eating and drinking can become a bit riotous, but always in very much a good humoured way."