Who is the King in The Hobbit?

[Pitchwife]

Without meaning to belittle the status of Thorin's family, I'd think Eriador was safely outside the jurisdiction of the King under the Mountain. A habitual allusion to the days of the Kings of Arnor seems much more likely.

[Legate of Amon Lanc]

I see no reason to counter-claim what's been said by some above in this thread a long time ago: it seems clear to me that what we are facing is the Hobbits' saying, as introduced in the Prologue to LotR. It seems obvious to me mainly because the words used are actually almost the same:

Originally Posted by The Hobbit

Others said: "These parts are none too well known, and are too near the mountains. Travellers seldom come this way now. The old maps are no use: things have changed for the worse and the road is unguarded. They have seldom even heard of the king round here, and the less inquisitive you are as you go along, the less trouble you are likely to find."

Originally Posted by LotR, Concerning Hobbits

There remained, of course, the ancient tradition concerning the high king at Fornost, or Norbury as they called it, away north of the Shire. But there had been no king for nearly a thousand years, and even the ruins of Kings' Norbury were covered with grass. Yet the Hobbits still said of wild folk and wicked things (such as trolls) that they had not heard of the king.

Especially with the trolls explicitely mentioned, I am inclined to think that this might have been even Mr. Professor's smooth explanation of his own unsmooth use of the phrase in the Hobbit several years ago, while later when writing LotR it became clear that there was no king in these parts of Middle-Earth at all.

As for the in-book perspective, it is interesting to note that by this logic (now you will see why I quoted the whole passages and not just the particular sentences), Bilbo must belong to the group of the "others" (which makes sense) - it was him, logically, who spoke these words (the question was the row between the travellers whether to go and check out the fire they saw in the wilderness or not). I considered it interesting from the perspective of the character analysis, as here we are obviously offered Bilbo's perspective on the matter put together into the group of "others" (some of the Dwarves), which by the way shows that he took an active part in the decision-making (resp. in the arguing) - which is nice, as I always pictured him as the fourteenth traveler who actually seems a bit misplaced and does not express much of his own feelings - at least not in public. This, on the other hand, sounds much more like the older, more self-confident Bilbo we know from LotR.

[Rumil]

Should one forget one's monarchy after a mere 1000 years, one would be no better than a foreigner,

toodle pip!

[Pitchwife]

Originally Posted by Rumil

Should one forget one's monarchy after a mere 1000 years, one would be no better than a foreigner,
toodle pip!

Is that the Welshman speaking, remembering the Owains and Llywelyns?

[Rumil]

Nah,

the Tudors