It isn't "stalling" but it is improving more slowly than the trend up to 2010.
There is some wiggle room in the word "stalling" that makes it a hard claim to be precise about. But showing the actual figures can help clarify the situation. Newspaper headlines and speculation about the possible causes of the "stall" have not usually contributed much clarity.
The BMJ however had a useful article earlier in 2017 which showed this chart which compares mortality to the level in 2001:
The article summarised:
On 6 April 2017 the UK Office for National Statistics released an analysis of deaths in England from January 2001 to the end of December 2016.4 It said that fewer deaths were registered in 2016 (491 000) than in 2015 and that the death rate in 2016 (958.0 deaths per 100 000 population) was the second lowest since 2001. Life expectancy in 2016 was higher than in 2015, and the number of deaths in 2016 was lower than expected based on the average death rate between 2011 and 2015 (973.3 per 100 000). Death rates have fallen among people aged over 75 since 2001, by almost a third for those aged 75 to 79, but “most of the fall was up to 2011, and there has been little change since then”.
In summary, it looks like life expectancy is still improving but since 2010 at a much slower rate than in the previous decade. So you could, at a stretch, call that a "stall" but it might be more accurate to call it a slowdown.
John Appleby, a respected UK health economist, posted this on twitter in response to some of the media noise (original tweet here, but he didn't quote the chart's source):
This clarifies that the trend is still positive, but much lower than before.
In summary, life expectancy is still improving but much more slowly than it did up to 2010. Call that a "stall" if you want, but you will probably just confuse things.