I have been hunting around to see which Greek manuscripts at the British Library it might be interesting to get digitised. It is remarkably difficult to find out.
The BL catalogue is online; but it is largely useless because there is no way to restrict results to Greek mss only. So a search for Chrysostom — every collection must have these — is pointless, because most of the results will be Latin manuscripts of translations. This is really quite frustrating. So far I have managed to find only a handful of mss which I might put forward.
One possible source of information would be Henri Omont, ‘Notes sur les manuscrits grecs du British Museum’, Bibliothèque de l’École des Chartes, 45 (1884), 314-50, 584 (p. 335). This is online here. Maybe this will list some interesting volumes, if it ever downloads!
UPDATE: Indeed it does. After a survey of the main collections, it lists the interesting previous owners and what they owned. I need to digest this down into a list of suggestions.