The selenium rectifier doesn't appear to have been overheated, a sure sign of failure. As they say, if it ain't broke...
What is the range of the ammeter? That will give you an idea of the current specs needed to replace the transformer (which appears to have a center tap on the secondary).
The "bi-metalic overcurrent cut out" (or its equivalent) should be replaced as well.
Although I admire your desire to rehabilitate the charger, unless you can find some used replacement parts, especially the transformer, the cost(s) are going to surprise you.