Just took the "The Táin" (admittedly thats quite old compared to modern historical science) in my hand and in Notes on the Text it states that:
That's not generally true outside the earlier period. There is nothing in the Táin which indicates Alba refers to Britain as a whole. In fact, some information indicates the opposite:
For if it were he who had come, armies and hosts and the pick of the men of Ireland (Ulster)who are with him would have come too, and even though the men of Ireland and the men of Scotland, the Britons and the Saxons were opposed to him in one place and one meeting and one muster, in one camp and on one hill, he would give them all battle, it is he who would win victory and it is not he who would be routed’
The writer here clearly distinguishes between the men of Scotland (Alba), and the Britons and the Saxons. If Alba had meant Britain here, then there would be no reason to mention the Britons and the Saxons as they would be included.
I'm not trying to argue that Alba never meant Britain (it definitely never meant Ireland or the Islands as a whole), but it was an anachronistic term for the 9th century, and certainly for the 11th onwards.
There seems to be no answer for certain. As far as i remember on a travel overseas to some witches in Wales they said to go to Alba as well.
Not sure if it was a travel by Cuchulainn or some one else, but part of the stories surrounding it.
That would be an interesting reference, if you have it handy.