sound like not enough air flow through the plant and the moisture/rain of late is tendng to sit upon the fruit and rot it.

When it is dry take a bag and pick off infected fruit put them in the bag to stop the spread. Doing it when it is wet helps to spread the fungus. It is Gray Mould or Botrytis cinerea. Leaving enough room between plants to allow free circulation of air is the best way of preventing this taking hold as Steveb says.