I don't think people will stop consuming meat if you ask them nicely. You have to make decisions that will hurt the meat industry and make it infeasible. This would likely best be achieved through slowly dropping tax incentives, and transferring them over to alternatives so that people have something equally economical to today's meat.
Millions of people are already voluntarily reducing their consumption and now virtually every restaurant in the UK has vegan options, making it easier for more people to switch.
I live in the outskirts of a relatively small, low-income industrial city and there are signs outside small shops and restaurants everywhere promoting their new vegan menus. A traditional pub near me has no fewer than 14(!) plant-based main courses.
I'd love to see tax incentives that reflect the damage that the meat and dairy industry are doing (ending the massive government subsidies would be a good start), however the changes I've seen in the UK give me hope that the grassroots level can sway public opinion without forcing people to change via legislation.