Both medicine and law are second entry, so an undergraduate degree is required.
Yes, those numbers have gone up. There's a great article that I would recommend to everybody, which is called “When Women Stopped Coding”. It describes the increase in participation rates of women in law, medicine, life sciences, and computer science until the mid 1980s, when the participation rate really dropped in computer science, relative to medicine and law, which are now pretty stable. Depending on where you are, it's roughly fifty-fifty, as it is in life sciences. Computer science was on the same trajectory—you can actually look at the data—and it dropped significantly.
The interpretation of those data are that media and marketing started it. The PC arrived on the scene, and it was marketed as a boy's toy. It became a cultural reference point that computers were for boys. Then we saw this drop off.