I have owned several milling machine vises. The first was a genuine Kurt. The rest were Asian copies. I have never had an issue with the movable jaw lifting. If the part is not square it will pull off one of the parallels when the vise is tightened. I do use a ball with a flat on it for clamping irregular work. The method of the work down is important. As others recommend, I always use some form of dead blow hammer. Lead is my first choice. I sometimes use copper. I tap gently while tightening the vise. It works almost all the time. Don't over tighten or you will deform the vise.
If Shars sells in the UK, I suggest checking out their products. My latest purchase was a 6" vise similar to Kurt. I is designated as a CNC vise. The sides are square to the base so it can be used on its side. The dimension are slightly different than Kurt, but Kurt jaws will fit.
Stefan Gotteswinter uses a toolmaker's grinding vise on the mill. It is calles a "screwless" vise. Actually the screw pulls the jaw downwad at about 45 deg. It had no jaw lift.