Mr Falkiner, who is an antiquities consultant both to the Ashmolean Museum in Oxford and also to Bonhams was among the first to inspect the vase in person when it arrived at the auctioneers' London rooms.
Strikingly similar to the Portland Vase, one of the British Museum's greatest treasures, it is larger, in better condition and with superior decoration, say Bonhams, who believe it could be the most important artefact of its kind in the world. Indeed, Mr Falkiner believes there is strong evidence that it is cut by the same hand.
Chantelle Rountree, head of antiquities at Bonhams, said: "It is of major international importance. Academically and artistically it is priceless. Scholars will be evaluating this find for decades."
The vase dates from between late first century BC and the early first century AD and stands 13in (33.5cm) high. Only 15 other Roman cameo glass vases and plaques are known to exist today.
These very rare vessels were highly accomplished luxury items, produced by the Roman Empire's most skilled craftsmen. They are formed from two layers of glass - cobalt blue with a layer of white on top - which is cut down after cooling to create the cameo-style decoration.
Items of this kind were produced, it is thought, within a period of only two generations. They would have been owned by distinguished Roman families.
Until now, the most famous example has been the Portland Vase. This is smaller, standing at only 9in (24cm) high. It is also missing its base and has been restored three times.
The recently identified vase is also more complex than others of its kind, being decorated with around 30 figures and a battle scene around the lower register. By comparison, the Portland vase has just seven figures.
Bonhams' experts believe that this magnificent artefact could rewrite the history books on cameo vases. Unlike the Portland Vase, it still has its base and lower register and will therefore add significantly to the archaeological understanding of these vessels.
The vase is thought to have resided in a private European collection for some time. The collector is a long-term client of Bonhams.
Mr Falkiner, a long-standing vetter of antiquities at the Grosvenor House fair, told ATG: "As far as I can see, the repairs make it look as though it has been out of the ground since at least the 18th century, possibly the 16th."
Bonhams say that, in co-operation with leading experts in the field and with the present owner of the vase, they will be carrying out detailed research over the coming months into the historical background of the vase and its miraculous survival, as well as into its more recent history and chain of ownership.
The vase was presented publicly for the first time at the 18th Congress of the International Association for the History of Glass at Thessaloniki in Greece in September, where it was viewed by around 200 of the world's leading glass specialists.
"The presentation created huge excitement among delegates, who were drawn from the world's leading museums and cultural institutions," said a Bonhams spokesman, "and there is no doubt about its authenticity."
By Ivan Macquisten