Washing Machine Magic
Or "Dishwasher Magic", or any of the various other products sold to remove limescale deposits, soap scum build-up and "clean" insides of washing machines and dishwashers ought to do the trick. However as previous poster stated porcelain enamel is harmed by acids (it was desgined to resist alkaline laundry products), thus you may loose or damage some of the tub finish.
Being as the above may, when my Whirlpool arrived, gave it a cleaning using two bottles of "Dishwasher Magic" settng the washer on high fill and using hottest water the taps could provide. IIRC let the machine agitate for 10 mins, then soaked for one hour, then let the machine drain followed by several rinses. Tub was clean, pump and between the tubs was flushed out, however the surface of the inner tub felt slightly "rough", almost like fine sandpaper after this treatment. Several subsequent wash loads with powdered detergent has restored the smoothness, and won't be doing that again any time soon.
If you do use the above treatment, use gentle agiation to prevent the acid treated water from splashing up onto the inside of the lid and onto painted surfaces around the opening of the tub.
Again, IIRC, some memembers recommened a type of polish one could apply to porcelain enamel tubs after cleaning to keep them smooth and protected.