As they say. Tell a lie enough times, and people will believe it's the truth.
I was just trawling through their site and found this recent press release:
A study measuring the impact of England’s smokefree law on hospital admissions for heart attacks has shown that the legislation resulted in 1200 fewer emergency admissions to hospital in the 12 months following the implementation of the 2007 law.  This is the latest of a number of studies measuring the short-term health benefits of smokefree laws  and the first to evaluate the impact on heart attacks in England.
This has been trotted out on various occasions since the smoking ban came into force.
The fact is that there has been no significant change since the ban in 2007. The downward trend was already well established. Most likely for a multitude of reasons.
The simplest way of showing this is by the use of the actual data in the study:
Emergency AMI admissions in English hospitals
2003/04: 60,680 (a fall of 1.33%)
2004/05: 58,803 (a fall of 3.1%)
2005/06: 55,752 (a fall of 5.19%)
2006/07: 53,964 (a fall of 3.21%)
2007/08: 51,664 (a fall of 4.26%)
To me the figures speak for themselves. I think ASH should stick their figures up their pipe (I.e. the fundamental orifice in their backside) and smoke them.