I don't know much about falconry but I haven't noticed any reference to use of EOs for that purpose in UK (but plenty to various falcons and hawks). I had the idea that some of the 'gentry' in the 18th-19thC liked to keep them as zoological curiosities or for status. Whatever the purpose, perhaps it's telling that they had to be imported.
The historic bird names issue is puzzling. The article "The Ornithology of Anglo-Saxon England" by Frank Stanford (
http://www.tha-engliscan-gesithas.org.uk/birdlore/fugsrc.html), cited in the Melling
et al BB paper, states that the EO "...named in Old Latin to Old English glossaries from the 8th century could have occurred in the extensive Anglo-Saxon forests". Note the "could have". The name listed is "Uf" or "Huf" and the author's suggestion that it refers to the bird's deep call is plausible given "Uhu" and similar names current in mainland Europe.
Of course, nobody actually knows if the 8thC name in fact referred to the EO call, but even if it does, perhaps it was added by a scribe who had travelled in mainland Europe (and many had). I may well be wrong but it seems that unless there is a clear descriptive element (eg. "Hwitars" for Wheatear!) there is a huge amount of guesswork involved in assigning these early names to Linnaean species, and I'd prefer to see some more solid reasoning before accepting this as evidence for presence of EOs.
Set against this is the apparent absence of any clear reference to Eagle Owl in folk culture or later descriptive or dramatic literature, and the absence of EO remains from Roman period and later archaeological sites (interestingly, re another debate, there is Sea Eagle material!) Seems a bit implausible that there could have been EOs present here a thousand-plus years ago without anyone anywhere having written down a few words about such a large and dramatic creature.
Whether the EO is a 'native' species or not of course depends on where the time threshold is drawn. Haven't got direct access to the literature on EO bone material but if it is dated to about 10,000 years before present, that would place it near the period the last glacial phase was ending and being replaced by warmer conditions. But given recent findings about the North Sea 'Doggerland', which wasn't submerged until about 6,000 years before present, the EO bones pre-date the latest separation of the British Isles and the European mainland. Whether that weakens or strengthens the case for 'native' status depends on your definition.
Don't think there is any reason to exclude the possibility of a dispersing or storm-driven EO reaching the UK after the species' apparent disappearance. But surely a relatively low probability, and as someone said above, even lower that a single EO would find another ex-mainland mate (or even ex-captive). With so many captive birds in the country it's got to be a much higher probability that EOs now in UK are escaped or released ex-captives.