I have three generations of barge builders in my family tree, the Ayles family of Rotherhithe.
A Thames barge is a completely different beast from the familiar narrow canal barge. The Thames barge was much wider and was used to ferry goods from ships not tied up to the dock side to the docks. They were latterly diesel powered, but with less labour intensive handling method and increasing mechanisation, they disappeared from the 1950s.
I believe barge builders had to serve an apprenticeship and records are kept in the Guildhall library in London.
I live quite a long way from London so I have not used this resource yet but I understand this library is open to the general public.