I had a good question which I have been wondering about for a long time, and as this week's theme is "Exploration and Discovery" I though I may as well ask now.
I am talking mainly about the use of Marine Chronometers and Lunar Tables.
and
Did other countries mount similar 'competitions' such as the 1714 Longitude Act which offered monetary rewards for a solution to the Longitude problem.
I am not aware of competitions other than the Longitude Act in other countries. EDIT: There were competitions in other countries.
In any case, the theory of longitude (that is, that the earth is spherical, and that local time differs at different parts of the earth) is ancient. Many countries (or, rather, theorists in many countries) other than Britain understood how to determine longitude with astronomical observations; the trick was being able to do that accurately on a moving ship.
You may be interested in these two older answers of mine about determining longitude.
From memory of reading Singh's book, yes, both France and Spain did.
From Wiki's sources it seems I was right.