Do you mean the plastic boxes besides the veg beds? If you do they are unsuitable for potatoes as the light will get to the tubers making them green and poisonous. Also it's still a little cold outside, my potatoes are still chitting in the conservatory not going out till the weekend. It is still early to see any growth outside.
The problem isn't that they're plastic, it's that they're transparent (I grow mine in halves of old water butts and it works fine).
No. Complete darkness is what they need or they go green. The foliage needs sunlight to photosynthesise but there should be no light on the tubers.
Then they should be OK altho I don't see much room for earthing up so make sure you keep an eye out further down the line and pour compost or soil over any exposed potatoes.