Please advise me on cleaning a white linoleum tile floor?

Magic eraser will really deep clean and make the white outstanding.

Use a dish liquid and baking soda in your warm water. Keep rinsing your mop to make sure you are not moving the dirt around.

Try Scrubbing Bubbles.

I have my whole house tiled and use nothing but a microfiber mop and plain water. Works great. If you get something really sticky or greasy a little Dawn to clean the spot. My microfiber mop heads are green, got them at a home show (Star Fiber) very knubby, clean the grout great also. I will try to attach a photo. The mop head on the top is an older one. This works great on tile and linoleum. I had white linoleum before I installed the tile and the microfiber was the only thing I used. Quite obviously, I swear by these. Good Luck.

I did see that these are available on Amazon.

I have a patterned vinyl tile in my kitchen. Once a week I use a few squirts of Dawn dish liquid to one gallon of hot water. Once a month I use one cup of lemon scented ammonia to one gallon hot water to get the embedded dirt, grime, and old wax off. Then I use Mop and Glo to give it a nice shine.