The arrests came after an air show
The 12 Britons and two Dutch nationals were remanded in custody on Monday, after being arrested for allegedly taking photographs inside a military base following an air show.
Two officers from the Greek national security department are now said to be assessing the group's photographs and notebooks.
Lawyer for the Britons, Yiannis Zacharias, told BBC Radio 4's Today programme that security forces arrested the group because they thought they were "looking and acting suspiciously".
The group have denied taking photographs inside a restricted military zone, a charge which carries a maximum 20-year jail sentence in Greece.
The lawyer added that British diplomats were spending a lot of time with the group, who are being held in a jail in Kalamata in the southern Peloponnese.
An assessment of the material seized will this week be sent to the magistrate, who will either set a trial date or drop the charges.
British consul Donald Holder said: "The assumption is that if there is no evidence against the people they will be released at that point.
The Greek authorities are aware of the fact that we would like this to be brought to a speedy end."
Organised tour
The charges were increased to full-blown espionage after, the Greek authorities allege, notebooks were seized containing details of other airfields.
The offence is often treated harshly in Greece because of longstanding military tensions with Turkey.
British diplomats had expected the court would view the whole affair as arising out of a misunderstanding about what the hobby of plane-spotting involves.
The flying club members were travelling with an organisation called Touchdown Tours.
Paul Coppin, from Mildenhall, Suffolk, runs the tour company and is one of those being held.
Others detained include Peter Norris, 52, of Uxbridge, west London, Wayne Groves, 38, of Tamworth, Andrew Jenkins, 32, from York, Mick Keane and Steve Rush, the Foreign Office confirmed.