[paul cotter (OP)]

It's very cold in the British isles and much of mainland Europe at the moment. When it lifts it will have been here for two weeks. Is this caused by the jet stream? Also to what degree does the jet stream affect terrestrial weather versus terrestrial weather affecting the jet stream?

[alancalverd]

I think the answer is "quite a lot" but I seriously doubt if anyone has any better numbers!

The atmosphere is inherently chaotic as a consequence of the "hairy ball" phenomenon, the random distribution of land and sea, the presence of water in all three phases (with huge energy exchange and thermal inertia between phases), and the fact that it is heated and cooled unevenly in all directions as the planet rotates on an axis tilted with respect to its slightly elliptical solar orbit.   

Just to add to the fun, the British Isles receive fairly constant warm water from the Gulf Stream on one side whilst the land mass of Europe alternately boils and freezes on the other; we happen to be at a latitude  where (in an idealised model) the opposing Hadley and Ferrell convection cells coincide; and the mean winter temperature is close enough to 0°C that a small change in surface temperature makes a huge difference  to the nature of precipitation and subsequent albedo.

In consequence all we can say with certainty is that the jet streams generally blow from west to east with all sorts of wiggles, and the weather in the British Isles is extremely difficult to predict more than a week ahead! Long term observations suggest that your best bet is that tomorrow will be a bit like today, as the dominant (warm) Atlantic low tends to drift eastwards at about 30 mph (bringing a diluted version of whatever happened in the eastern USA 3 days ago)  and the occasional (cold) Arctic high persists for around a week at a time.

[vhfpmr]

The big freeze of1963 here:
https://www.bbc.co.uk/iplayer/episode/b01q9d86/winterwatch-1963-the-big-freeze
(explanation from 43m18s)

I don't know what temperature it got down to in the 2010 freeze, but I was going out on the bike with water bottles filled from the kettle, and coming back 3 hours later with them frozen.

[Bored chemist]

Can you even have a prolonged "snap"?
Our Russian or Canadian friends  would, I think, wonder what you are talking about.
For them, Winter starts when Autumn finishes and it's damned cold for 3 months until Spring arrives.
Our weather thanks to the interplay of convection cells and the gulf stream, changes more or less hour by hour in a way that provides us with so much to talk about.
We never get a prolonged spell of anything.
But, having got used to weather that changes twice a week, when it stays the same for a fortnight, we think something weird is happening.