Can I brighten up the old porcelain ceramic tile in my bathroom?

I live in a bungalow built in 1945, and the bathroom is larger than most of that era. I want to keep it as intact as possible. The lower half of the walls, tub surround, walk-in shower, and the floor still have the original white-with-black-trim ceramic tiles. The white is dingy. Is there a way to restore it, and the grout, to its original color (or as near to white as possible)? The tiles are glazed, btw.
 
A very sensible question, so rare for Answers. Unfortunately, I am not handy but I think Tips from Heloise may help, just google 'tips from heloise' and there's a lot there that should address it.
 
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