Color Finesse (included with After Effects) has an auto white balance feature, and also has a white-point sampler that works as you describe.
Apply Color Finesse to your layer, click the Full UI button, then click the Levels tab within Color Finesse. You'll see both the auto white balance button and the white-point sampler eyedropper there.
Of course, like all automatic processes, your mileage may vary. Depending on the original cause of the "bad" white, sometimes you can get a perfect white but everything else is now "bad."
Finding perfect white is always a challenge and it may foul up other things in your shot because white walls are reflective and if someone is wearing a blue shirt against a white wall, white may not be white. Setting white may get you in the ball park, but it is usually only the first step in color grading. You usually want to push highlights to one hue and shadows to another.
The procedure and the tools used to color grade a shot depend entirely on the shot. For most of my work Colorists II is my preferred tool. Some shots require more than one instance of colorist to get to where I want to go. Color finesse is also good, but for some work, and this depends entirely on the shot, Auto Color is all that I need. No matter what technique you use to grade your shots you need some kind of scope or histogram that you understand so you can know where you are pushing the levels in the shot. I'm always checking areas of a shot with the Info Panel to make sure I know what I've done to the color values. Most of all, good color grading takes time to learn and a very thorough knowledge of color.
Yet another way is to use the CC Color Neutralizer effect built into After Effects.