But that’s not how we designate authors in the field. When you’re discussing the various literatures in English, nationality in the political sense is effectively meaningless. Robert Burns was born in Scotland after the Act of Union of 1707, but no one refers to him as a “British poet.” He’s Scottish. Likewise, Heaney is an Irish poet, David Jones is a Welsh poet, and so forth. Those distinctions matter within the field of literary study, so it’s not really even a matter of being “pedantically” correct. It’s simply not how we classify authors within the various literatures that generally fall under the umbrella of “English literature.” To call Stoppard an English playwright (rather than a Scottish or Welsh or American playwright) has a significance in identifying the particular tradition within which he works.

Moreover, England, Scotland, Wales, and Northern Ireland are recognized as constituent countries of the United Kingdom. (And is should be noted that “Great Britain” only encompasses England, Scotland, and Wales—not N. Ireland. So it’s definitely incorrect to refer to a N. Irelander as “British.”) They aren’t simply states in the way Texas or Tennessee are. They are countries with devolved governments, and are recognized as such by the UK government. As such, it seems entirely fitting, even from a political and pedantic standpoint, to refer to someone as belonging to the particular country from which he hails.

E: Probably also worth noting, since we’re being pedantic, that OC’s comment that “the man is quite English” need not refer to his nationality per se. It could just as easily mean that Stoppard is culturally “quite English” rather than indicating which national gov’t issues his passport.