I was happy to receive responses from two readers which are helpful, I think, and I reproduce them here.
The first is from Bishop Jerome, Bishop of Manhattan of the Russian Orthodox Church Outside Russia and this seems to summarise the situation nicely. He says:
The reason that statues are avoided in the Orthodox Church (and in some of the Eastern Catholic Churches) is not that they were seen as "heretical", but as part of the struggle to overcome the iconoclasts. Prior to the iconoclastic controversy, there were bas-relief representations of holy figures in the East, and in Russia the iconoclasts seem not to have been as virulent as they were in Constantinople. 3-dimensional figures were used to some extent again in Russia in certain places, such as the cathedral of the Ss. Peter & Paul Fortress in St. Petersburg, where the Royal Gates were topped by a small statue, or in the dome of St.Isaac's cathedral where there are statues of Angels.
here (h/t Fr Anthony). This gives some history of the creation of statues, reinforcing the summary of the situation given above by Fr Jerome. It closes with the following point: 'The 1920’s discovered the Orthodox painted icon, the 1970’s the Orthodox statues. It appears the sometimes heated "two dimensional vs. three dimensional image" argument could be another example of culture intruding upon the faith.'
This second article brings up a couple of interesting thoughts. First, some of the examples that are shown in the pictures are of statues East and West. This shows clearly that the tradition of statues was well established early on and not always a minor part of the sacred imagery as it became later in the Eastern Church. It also reinforces one of the points made above. It does seem to me that a strict application of the theology of the icon as I have been taught it, would mitigate against the production of three-dimensional images. But the existence of a strong tradition of statues raises this question in my mind: if the statue which by its nature occupies three-dimensional space is permitted, does this mean that there ought to be greater freedom in 2-D images that create the illusion of space? Has anyone thought about this at all I wonder? Perhaps one could, for example, make the distinction between real 3-D space and illusional space critical in permitting statues?
Pictures from top: the Good Shepherd, 3rd century from the catacombs; 10th century Contantinople; Our Lady of Monserrat, Spain, 12th century.