I hope you'll forgive me if I sound callous in this post - I certainly don't mean to, but I also recognise that this is a touchy subject when talking about someone's own family.
In the case of your great-uncle the problem is likely that it was the 70s and fourty years ago there was nowhere near the same awareness of the symptoms of cardiac arrest amongst non-physicians. If the doctor wasn't there, chances are it wouldn't have been picked up on. Even had he been rushed to hospital, his chance of survival would have been pretty low - heart attacks are still a major killer in the 2010s where even in London, which has the highest survival rate in the UK for heart attacks that occur outside a hospital, the survival rate is only 30%. Keep in mind though that survival rates have increased significantly over the last fourty years with advances in diagnostics and treatment as well as improved defibrillators etc.
Your grandmother's case is a more clear cut case of failure. Waiting times have long been a problem in the NHS, but it's a matter of resource contention, and it's a problem which they're trying to improve with the guarantee that patients should start treatment within 18 weeks of their first appointment and that tests should be done within six weeks. The only, very rough, numbers I can find for the US suggests that scans and tests are normally done within seven to twenty weeks when cancer is suspected. Even in the US, the problem of resources exists - there's only so many hospitals that can perform certain types of scans, and only so many doctors who are capable of properly interpreting the results. The thing I can't comment on is whether or not the physician who saw your grandmother should have treated it as a higher priority or if, given the symptoms that were presented, it would be reasonable to assume that there was a benign cause and it being cancer was pretty remote possibility. If it's the case that his prognosis was obviously wrong given the symptoms, then there's a case to be made for malpractice, or at least a complaint to the GMC and/or NHS trust.