Step 1: Understanding the Concept:
The question asks to identify the primary administrative and regulatory authority established under the Trade Unions Act, 1926. This Act provides for the registration of trade unions and defines their rights, liabilities, and immunities.
Step 2: Detailed Explanation:
The Trade Unions Act, 1926, provides for the appointment of a specific authority to handle the key functions under the Act.
\begin{itemize}
\item Section 3 of the Act empowers the appropriate Government to appoint a person to be the Registrar of Trade Unions for each State.
\item The Registrar is the principal statutory authority under the Act. The main functions of the Registrar include:
\begin{itemize}
\item Registration of trade unions (Section 8).
\item Issuing a certificate of registration (Section 9).
\item Cancellation or withdrawal of registration (Section 10).
\item Receiving annual returns and ensuring compliance with the Act's provisions.
\end{itemize}
\end{itemize}
The other options like "Regulator of trade unions" or "Inspector of trade unions" are not the official designations used in the Act. The correct and official title of the principal regulator is the "Registrar of trade unions."
Step 3: Final Answer:
The Principal regulator envisaged under the Trade Unions Act, 1926 is the Registrar of trade unions.