One would have a strong argument that the American Revolution of 1776-1783 and the Ameri-British conflict of 1812-1814 were largely "Gentleman's Disagreements" rather than full-fledged conflicts. Of course the Mothers that lost their Sons in the ensuing battles would disagree... but the reality is, The USA and the UK are by far-and-away the most integrated political bodies in today's world from a military standpoint. We have so many (still valid) military agreements and treaties, dating all the way back to the 15th century, from a strategic point of view our communities, in reality, never ceased to be one.
Which brings up the whole UKUSA Agreement, which by its very name embodies the core of the intense and deep security integration you speak of. Sure, with the UK set to exit the EU, mainly because of the desired tax on financial transactions which would basically disrupt the City of London and amount to a massive transfer of power towards Brussels, the time may come to discount Obama's "at least 10 years to negotiate trade deals", and start looking at something like a formal alternative to their association with continental Europe. One would not be blamed for thinking that a Trump presidency would dramatically speed up any such realignment, bypassing the resistance of humanist inclined bureaucracies who wish for the UK to remain within the EU (a.k.a the flagship humanist project).
"Entre le fort et le faible, c’est la liberté qui opprime et la loi qui affranchit." - Lacordaire