Actually, both the US and the British agreed to the so-called Utrecht line in 1818--and had in fact agreed to it much earlier, in the unratified agreements of 1807. "In the negotiation of 1818 Albert Gallatin and Richard Rush were the American plenipotentiaries. They were, like their chief, under the influence of the idea of a Utrecht line... [Their argument for using this line to divide Oregon was that the line] was already the boundary separating British and American possessions for a great distance east of the Stony [Rocky] Mountains...[That this was the case] was not challenged by the British plenipotentiaries, both alert persons, Frederick J. Robinson and Henry Goulburn [who merely objected to *extending* this supposed line to the Pacific, insisting that instead the Columbia be used as the dividing line west of its intersection with the 49th parallel]."
https://groups.google.com/d/msg/soc.history.what-if/bZRQvBa_UAw/3qBrGR5M18sJ
As I argue in that post, the so-called Utrecht Line may have been based on a misreading of history--but if so, it was a misreading shared by both sides. The only dispute was its application to Oregon, and that was not resolved in 1818 anyway.