Personally I think that it would be better to make animal slaughter illegal as to the extent which is possible. I feel that this would help to improve their conditions. However I am also aware that many would disagree with this, as not everyone would be willing to stop eating meat/other animal products.
Thus I would like to know whether there are cases where a government banned animal slaughter and was also able to reduce it, at least to a limited extent.
I am pretty sure there has never been governmental (or feudal/whatever) ban on animal slaughter and/or consumption, so I do not see your original question being answered. There can, however, be some approximation by looking at other huge organisations (such as religions) which do at times promote such bans. There is also the possibility of answering based on speculations with basic human psychology and precedents.
The religion angle. While religious organisations have arguably smaller executive power than governments these days, their impact on human behaviour is still profound and the effectiveness of a ban of anything demanded by religion might meet with more success and less resistance, merely because of the devotion thing. Luckily, both for the purposes of this answer and for the lives of countless animals, there is a major religion that promotes this. Hinduism. While vegetarianism is not required in Hinduism per se, the principle of nonviolence is an integral part of the teaching and an estimated 30% of Hindus are vegetarians. Pretty good numbers, considering that it is not even required, as compared to outright banned. While some non-Hindus are also vegetarians, Hinduism and other traditional Indian philosophies can be argued to be the biggest factors in making India the country with largest number of vegetarians in the world, both in percentage and numbers (in the reference, there is the Brazil entry claiming some pretty big claims, but it is unquoted and likely misleading). As for the second part of your question, the positive impact of this on the animals, well, it sort of follows.. Less people eating animals = Less animal death. Less animal death = positive impact on animals, since they don't die that much.
The precedents based, psychological angle. Another way of looking at this and trying to determine the answer can be based on similar past bans of stuff popular among population. In general, when something is banned, there is a negative external pressure on your motivation to seek it out. Whether you still seek it out is therefore based almost solely on the strength of your internal motivation. Let's take a look at one of the precedents.
While using a methodology that can be argued against, the NBER estimation of the alcohol consumption during Prohibition shows some interesting trends. The alcohol consumption fell sharply to 30% of pre-Prohibition levels in the beginning. This tells us that approximately 30% of population had an internal motivation strong enough to ignore the ban from the very beginning. Arguably, these would for example be the alcohol addicts or the adamant Prohibition/government opposers. The remaining 70% was a mixture of people with little or no internal motivation to breach the ban, eg. occasional drinkers and people who had some levels of internal motivation, but which were sufficiently affraid of the punishment that would follow the breach. After the initial sharp decline, when the murky waters of 'how strict this ban is anyway?' were sufficiently explored, the consumption rose to 60-70% of the pre-Prohibition levels. Merely by probing the strength of the ban and after the whole Prohibition economy blossomed and became sort of a public secret, some people found it beneficial enough to ignore the ban and go back to drinking. After the Prohibition ended, the levels eventually (not immediately though) rose back to the pre-Prohibition levels.
Now, to draw some lines back to the animal slaughter ban from all this, there is a couple of variables to consider. There is the addictivness one, with alcohol having an upper hand here as a certain percentage of population ignored ban simple because they were not able to do otherwise. If animal slaughter ban were to be enforced, there would probably be much smaller number of people having this problem, if any. Then there is the popularity one. Both alcohol and meat are popular enough, although the meat has undeniably bigger audience. It is ingrained in most of the cultures in a way that alcohol can hardly ever be. Alcohol and meat 1:1 so far. From the health point of view, alcohol is a clear loser - what is interesting though is that, nonetheless, people actively looked for ways of consuming alcohol even after it was banned, even though it was detrimental to their health. The ban therefore did not have much impact on the public perception of the intrinsic reasons for the ban itself. If meat was to be banned, the environmental and ethical aspects of the ban would therefore likely to be ignored just about the same as before the ban, at least for the beginning. More on that later.
I could continue for quite some time, but let's be concise. I think if a meat ban was to be imposed today by government in one of most of the countries, it would initially follow a similar path to that of alcohol during Prohibition. A sharp decline in consumption, based on initial fear of punishment, followed by a steady increase as the illegal economy seizes the opportunity and the borders of acceptable are probed. I believe, however, that the ban would see the meat-eating percentage of population reduce much more than the 30% that we saw during Prohibition, simply because of the non-addictivness of meat. The increase would also be smaller (it doubled with alcohol, it could easily double here too, but smaller number doubled is.. a smaller number). The final outcome (which for Prohibition was an end and the return to the previous state) would largely depend on two things. The reason for government to issue such a ban - it would be possible to assume that there was already a public pressure on the government to do so, as there is very little incentive for it to ban it otherwise - and the length of the duration of the ban - the longer the ban would be in place (say a couple of decades as opposed to a couple of years/decade) the more profound and longer lasting would its impact on the meat-eating be. Generally, people are surprised with how easy and natural the transition to vegetarianism/veganism is. If they were legislated into it, it could eventually become part of the social norm and eating meat would then be largely perceived as wrong. The ban would eventually transform the legal issue into a moral issue and that is much more likely to last, even if the ban was overturned.
Again, the positive impact part of your question seems apparent to me and I won't go into it here.
A lot of this is, of course, speculation, but it is one that I wanted to make. It is possible that your question will get closed as unanswerable, since it basically is, but it opens up an interesting debate. Unfortunately, this is not what this site is for - you might want to visit our chat if you would like to debate.
In 675AD, Japan forbade the killing of animals for meat, due to the adoption of Buddhist beliefs.
This, while not perfectly observed, did result in a significant cultural change over the next several hundred years until western influence entered the region along with their associated diets.
We can only suppose this helped animal welfare, but the animals were still used for menial tasks, and for other products that did not involve killing.
Have you ever heard about the Animal Welfare Act in New Zealand?
The law is not primarily about the consumption of meat in the sense of eating. However, if you take a broader definition of consumption then the "ban" of animals for cosmetics testing might go in the direction of what you were looking for.
I am putting "ban" into quoting signs since it is - as you have anticipated in your question - doubtful if the law will in fact change the practices in the industry.
See for example this link for a more critical view on the law.
