Egypt, Syria, Greece and the Balkans were all part of the Byzantine Empire, and the final three were part of it until quite late, so they did not lose the Roman/Hellenistic level of literacy they had had. Alexandria, in particular, although it declined from its height around the turn of the millennium, remained a centre of learning for a long time. Also, of course, they ceased to be part of the Byzantine empire through being conquered by the Muslims, who also had a literate civilization.
Even in western Europe, there always remained some level of literacy, at least amongst the higher levels of the Catholic Church (although parish priests were often illiterate, I believe), and amongst monks, who had to learn to read and write at least at an elementary level in order to copy manuscripts. Manuscript copying was part of the rule of St Benedict, and all monks had to do it. However, it declined a lot amongst the secular, largely because the barbarian invaders who had overrun the Western Empire (including Italy) were not literate when they arrived. I do not think Britain had it any worse than Iberia, Gaul or Italy. Indeed, literacy hung on in places in Britain through the darkest of the dark ages. The rulers employed literate people from within the Church to run their bureaucracies (which probably goes a long way towards explaining how the barbarian invaders became converted to Christianity). Most notably, Charlemange, although probably illiterate himself, organized a huge program of copying of classical manuscripts.
Even at the height of the Roman period, however, I think you will find that literacy, although common amongst the upper and middle classes, was far from universal even amongst Roman citizens.