the second in the glorious revolution with the Netherlands in 1688.
I have to point out that this example is a bad example as it had nothing to do with a PU. The situation is far more complex but Willem III saw a chance to 'upgrade' from being stadholder of a state which was after extensive, sequential wars int he second half of the 17th century ,arguebly, on the edge of collapse (First anglo-dutch war, second northern war, dano-swedish war, war of devolution, franco-dutch war, third anglo-dutch war, second swedish war on bremen, second anglo-dutch war, scanian war etc.) to a country with more potential.
However, back to the OP. GB is quite strong already and its able to focus almost solely on the naval aspect (while other naval countries have to focus on army as well, such as the netherlands or spain). Therefore, I disagree on the need to change them, especially because one can not judge what effect mare notrum will have on their relative power.