Most slaughter houses in the UK do a good job. It is difficult/impossible to slaughter an animal in a way that does not cause it stress. This is because slaughter almost always involves transport, a novel environment, new handlers, a need to stick to time parameters, an industrial system etc. However, in most slaughterhouses I would say that this stress does not tip over into suffering. Suffering is never acceptable and in my view there is no such thing as "un/necessary suffering" as no suffering is acceptable. There are many things that can be done to reduce stress and lots of people take the time to do them.
However, most humans, going into even a good slaughterhouse would be shocked and horrified. This is because most people are very far removed from the meat they eat actually being an animal, have no concept of what industrial agricultural practices look like, and instinctively recoil from them. I believe that if slaughter houses had glass walls the consumption of meat would fall. But that is not a fault of the slaughterhouse as such, it is the wilful ignorance of consumers.
However, there are a small minority of slaughterhouses which do not operate in a good way. Either 'legally' by having exemptions from stunning, or 'illegally' by poor practices.
The biggest factor in determining the experience of the animal at slaughter, is the quality of the slaughterman. It is possible for somewhere with an excellent system and facilities to give a bad experience, and it is possible for somewhere with a bad system and facilities to give a better experience than you might expect. However, somewhere with good facilities/system always has the potential to give a better experience, all other things being equal.
For this reason I believe all slaughterhouses should have CCTV installed. I believe there should be no loopholes to avoid stunning, and I believe that figures of mis-/failed stunning should be recorded so that action can be taken to reduce the instances and research even better methods.
Slaughter is a very small part of the life of a farm animal. People should be far more concerned about the overall life of an animal (including slaughter). We have an increasingly industrialised farming system in the UK and around the world. 70%+ of farm animals are raised in factory farms. Pork and poultry is more likely than not to have come from factory farming systems. That isn't to say lamb and beef don't have their issues, but in general they offer a much better quality of life for the animal. Most people would be horrified if they saw the inside of a factory farm, but again wilful ignorance plays a massive part.
Again, much comes down to the husbandry skills of the farmer, but an extensive system has much better welfare potential than an intensive one. Factory farming also has detrimental impacts on the planet and human health.
For this reason I believe that all meat and dairy should be labelled with method of production. I believe people should buy from a local source where there is a clear route from farm to fork. If that is not possible, they should buy British, and not buy pork or poultry unless it carries a label that ensures higher welfare.
Finally, I believe that the majority of people who read these stories in the DM and the Sun don't actually care enough about animal welfare to make the changes in lifestyle that responsible sourcing of food entails - they might pay lip service to it, but actually doing something that inconveniences them/costs more? Unlikely. They do like an opportunity to chunter about the Muslimisation of Britain though, and the editors and those pulling their strings know this perfectly well.