Pretty much. A lot depends on how nitpicky you want to be, but the notion of competing Anglo-Saxon kingdoms ended with the fact that Alfred ended up ruling all non-foreign-occupied parts of what we now call England. He was the legitimate claimant, his dynasty drove out the foreigners, and thus England was forged. One can argue that his grandson Æthelstan was the first, because he conquered the Viking Kingdom of York and with that conquest finalised the unification of the Anglo-Saxons... but hardly anyone uses that as the big starting point.
If people really wan to be nitpicky, they can argue that the first "king of England" was actually Henry II, since he was the first to call himself 'Rex Anglie' instead of 'Rex Anglorum'... but that would mean William I, William II Henry I and Stephen of Blois weren't kings of England either (instead being just 'Kings of the English'), and should be discounted. Basically, if you're going to count Kings of the English, you should also count all Anglo-Saxons kings as of Æthelstan-- who first came up with that title. And then the concept itself is clearly more important than the exact title used at the time, which means that besides the Kings of the English, the Kings of the Anglo-Saxons (essentially just Alfred the Great and Edward the Elder) should also be counted.
This is the reasoning most people seem to use, and the one to which I also subscribe. I can
understand leaving out Alfred the Great and Edward the Elder, but if one seeks to be consistent, one must then start with either Æthelstan or with Henry II. Since the very idea of considering someone called 'the second' to be the first is patently absurd, Æthelstan would be the sensible choice. (But just starting with Alfred is still better.)