We still have some white plastic chairs and a table which are yonks old and they are still in excellent condition, mainly because we stack the chairs, and cover both them and the table with a waterproof cover at the end of each day's use and wipe them down to stop any stubborn stains becoming permanent. This also helps to keep them white, rather than going a cream shade. However, if the damage is already done, neat Liquid Flash (I use the lemon one but assume they're all similar) can be very effective. Just pour a little on the dirty marks and leave for a few minutes before wiping off. Protect your hands first though as it can strip all the oil from your skin.