Some info on the last time this happened.
http://en.wikipedia.org/wiki/Maunder_Minimum
I've never given a lot of credence to the global warming theory. It really boils down to the sun and its output...sure, it only varies by fractions of 1% but the climate of the world is so delicately poised that even tiny amounts make a huge difference. The general feeling among climatologists is that we are living in a "warm" period, but these are usually short lived and "cold" is the norm for planet Earth. The main concern would be that melting ice sheets would alter ocean currents and The U.K would no longer be under the influence of the warm Atlantic current, without that, we'd be looking at a climate similar to Alaska . Little is known of the timeline of Ice Ages, but if the Gulf stream was disrupted it'd be pretty quick, last time it became disrupted was about 11,000 years ago.
http://en.wikipedia.org/wiki/Younger_Dryas
Pete