https://en.wikipedia.org/wiki/Royal_Mail
The process started under the Labour governement really Mikey.
"After a change of government in 1997, the Labour administration decided to keep the Post Office state-owned but with more commercial freedom. This led to the Postal Services Act 2000, where the Post Office became a public limited company in which the Secretary of State for Trade and Industry owned 50,004 ordinary shares plus 1 special share, and the Treasury Solicitor held 1 ordinary share.[35] The company was renamed Consignia plc in 2001[36] and the new name was intended to show that the company did more than deliver mail; however, the change was very unpopular with both the public and employees. The Communication Workers Union boycotted the name, and the following year, it was announced that the company would be renamed Royal Mail Group plc."
In 2008 the recommendations in the Hooper Review led Business Secretary Lord Mandelson to seek to part privatise the company by selling a minority stake to a commercial partner. it was actually delayed though until Vince Cable took it forward