Atlantic currents seem to have started fading last century
arstechnica.com
arstechnica.com
Conceivably global warming could stop it, accelerate it, just be a nuisance term. We simply don't know.
One of the most important factors is the arrangement of the continents[1]. First, having a large polar continent allows ice to accumulate and increase the Earth's albedo significantly. Second, having two major oceans instead of one decreases the efficiency of heat transfer around the globe, allowing other pockets of glaciation to occur. In a scenario with no polar continents and only one major ocean a glaciation is virtually impossible regardless of where we are in the Milankovitch cycles[2], because the Earth is effectively swimming in a thermodynamic bath. Atmospheric composition is actually a relatively minor factor, it's just that human activity can't shift continents around or affect solar cycles and those both change on much longer timescales than human activity.
[1] https://www.wisegeek.com/how-does-the-placement-of-the-conti...
Seems like the UK might stay the same but be a bit dryer?