If the Gulf Stream collapses that will entail adverse consequences for me so notwithstanding it's the Grauniad let us have a look.

The first study found significant Amoc weakening after the end of the little ice age in about 1850, the result of natural climate variability, with further weakening caused later by global warming.

The second study suggests most of the weakening came later, and can be squarely blamed on the burning of fossil fuels

However, it is already clear that human-caused climate change will continue to slow Amoc, with potentially severe consequences. "If we do not rapidly stop global warming, we must expect a further long-term slowdown of the Atlantic overturning," said Alexander Robinson, at the University of Madrid, and one of the team that conducted the second study. He warned: "We are only beginning to understand the consequences of this unprecedented process - but they might be disruptive."

So we have a bunch of assertions to the effect that an observed AMOC weakening is caused by fossil fuel use.  Now you know by now what I'm going to ask for don't you.  The article also states

He [Dr. David Thornally] said current climate models do not replicate the observed slowdown, suggesting that Amoc is less stable that thought.

and

The [current] climate models don't predict [an Amoc shutdown] is going to happen in the future - the problem is how certain are we it is not going to happen? It is one of these tipping points that is relatively low probability, but high impact.

The models fail to predict it - in a truly shock result - so it apparently lies outside of what anthropogenic-driven climate science thinks it understands.  What then is the evidence in support of the assertion that this reported AMOC excursion is driven by human fossil fuel use?

In 2012 a study found an increase in heat transport from the Atlantic current was leading to increasing sea ice loss.

In 2012 a study found an increase in heat transport from the Atlantic current was leading to increasing sea ice loss.

Nonlinear systems are complicated! Complex even.

 There is a lot, and I mean a lot of research regarding the Atlantic ocean and climate change.  

The Atlantic period (Holocene climatic optimum) is thought by some researchers to be direct result of a warmer Atlantic, greater circulation, with more heat transport to the arctic regions, and especially northern Europe.  The  rising temperature and marine transgression are obvious in all kinds of records, from sea cores to ice cores to pollen and tree lines and such.  The sea rose to 3 m above its present level by the end of the period. Lake levels in all north Europe were generally higher, it was the warmest period in the last 110 thousand years.

The temperature rise had the effect of extending southern climates northward in a relatively short period. Short by geological times that is. The treelines on northern mountains rose by 600 to 900 m (2000-3000 feet). Thermophilous species migrated northward.  Across middle Europe, the boreal forests were replaced by climax or "old growth" deciduous ones.

There are theories that in fact the ocean circulation is the real driver of climate change, but caused by solar variations due to changes in the solar UV amounts, and orbital changes of the earth.  The boffins can't decide if the climatic optimum is an example of what AGW will cause, or not.  But in any case, we are not seeing the sort of changes yet that we know happened during the Atlantic period.

We do know, with out any question, that for some reason during the Atlantic period there was far less ice on Greenland, and it was much warmer than present. 

For your edification, "boreal forest" is another name for the Taiga

If we do observe the Taiga (pines, spruces and larches) being replaced by deciduous trees, we can be sure, with out any doubt, the climate is warming. 

Meanwhile, back in reality land

Tell me it's not true, FX!

Gulf Stream current at its weakest in 1,600 years, studies show

Wtf do you mean by "true" here?  The junk media article you reference is attempting to be alarmist about a study which is yet another CMIP5 GCM effort.  So if you want to believe that the output from a model ensemble with zero demonstrated predictive skill in a coupled nonlinear dynamical system may be ascribed the value "true" then that's your problem.

"This weakening is revealed by a characteristic spatial and seasonal sea-surface temperature 'fingerprint'--consisting of a pattern of cooling in the subpolar Atlantic Ocean and warming in the Gulf Stream region--and is calibrated through an ensemble of model simulations from the CMIP5 project".

Meanwhile all of the actual measured data gathered over recent years clearly indicates that AMOC is doing anything but slowing down.

https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2010GL042372

http://www.pnas.org/content/pnas/113/20/E2760.full.pdf

https://www.nasa.gov/topics/earth/features/atlantic20100325.html

This weakening AMOC trope is one of the many alarmist zombie 'facts' and they cannot ever let it go.  When the data flatly refutes it then as usual they go with a model which says whatever they want it to say and that is what the compliant media report.  Twice today I heard worried groups of people talking about the Gulf Stream shutting down because it's all over one of the most extreme propaganda falsehood machines in the world known as the BBC.

The junk media typified by the Guardian tirelessly seek out junk science typified by climate modelling in order to support their endless alarmist narrative and will go nowhere near actual empirical data which falsifies it.

More fake news from the Guardian

https://www.theguardian.com/environment/2018/apr/13/avoid-at-all-costs-gulf-streams-record-weakening-prompts-warnings-global-warming

Are they just trying to scare us?

(This comment contains some irony)

Are they just trying to scare us?

Not just to scare, but Yes they are.

They want you alarmed and scaref

Greenland's ice sheet is melting at the fastest rate in centuries!
    

But

Did the Greenland ice sheet grow in 2016 to 2017?

    

The best estimate is enough ice melted to raise the sea level by .65 mm