The Gulf Stream and North Atlantic Drift – which are part of the Atlantic thermohaline circulation – bring warm water, and with it warm air, from the tropical Atlantic to northern Europe. This helps keep the UK several degrees warmer than it would otherwise be.
Although this system is unlikely to pack up entirely, the IPCC deems a slowdown of it "very likely" over the next century. The reason is that increasing rainfall and snow-melt across the Arctic and nearby land areas could send more freshwater into the north Atlantic, pinching off part of the warm current. The best guess from the most sophisticated computer models is that the circulation might slow by 10% to 50% over the next century, if greenhouse gas emissions continue unabated. If this happens, the expected climate warming might be nearly erased across the United Kingdom and diminished across many other parts of Europe. However, summers could still be warmer and more drought-prone across the UK and Europe than they are now.
In any case, the impacts would be much smaller – and would take much longer to play out – than the scenario dramatised in the film The Day After Tomorrow. Although evidence shows that the thermohaline circulation has ground to a halt more than once in climate history, it's believed that this process takes at least a few years to play out, and sometimes many decades, rather than the few days portrayed in the film.