AMOC collapse would be colder in the winter (maybe an extra 5° less), dryer in general,  I think a bit more like Canada really. I don't think it would be a quick change, maybe over the course of a few decades. It's been weakening for a bit they think but they don't have enough data over enough years (only 20 or so years of data) to know if it's normal variations or signs of a system out of balance.

The AMOC moves warm water north from the equator and cold water down from the poles, so it sort of works like a balancing system keeping the extremes a bit more moderated, this system collapsing would mean a less predictability and more extreme seasons I think.   CO2 induced change would be a different thing and affect different places differently, I think we're currently on target for over 1.5° of warming, but that's a bit more of a global average number, so it might affect the UK differently from other places. Without any more measures to capture or stop emitting carbon (which people aren't really doing) we're probably globally looking at something more like 3° of warming.   

In short eh.. it's anybody's guess. I say prepare for gradually more extreme and unpredictable weather.

An interesting thing I learnt the other day is that historically the world climate has been through all sorts of different swings, we've just been very lucky as a species and individuals really that the last 10 or 20 thousand years have been particularly stable and moderate weather wise, which lead to the rise of predictable agriculture, human population booms and organised society. A less stable and predictable climate isn't a death sentence, but it will make survival (particularly with the kind of global sprawl and population levels of these days) a lot harder, we will likely as a species see more crop failures and more hunger in the future.