In the 1980s sitting Labour MPs found themselves in danger from the reforms the Constituency Labour Parties, CLP, were pushing through. The ability of the local parties to de-select their MP meant they could be pushed off the gravy train. (I heard Shirley Williams, no friend of left, describing how when looking for a constituency Tony Blair called the local party members 'comrade' to show what a good socialist he was. Re-selection does seem a good idea when faced with such blatant ambition and opportunism;-)
The Parliamentary Labour Party fought back against this attack on their job security and won. To win they had two big weapons. First a left-wing leader, Neil Kinnock, to take on the far left, and second, a good target for media in the Militant Tendency. He attacked them relentlessly and had them expelled from the party. From here on in the power of the CLP was drastically reduced and the PLP wrote the rules.
The birth of New Labour comes out of this destruction of the traditional balance of power within the party. It was not that much later that the power of the unions was also reduced. (The outcome of this we see today with all sleaze related to the major financing of the party by wealthy individuals instead of the unions.) With no opposition within the party the PLP was able to turn its back on Labour's history and any socialist ideology.
There are a few myths around that don't really stand up to scrutiny. First that Kinnock, Smith, Blair and Brown were making the party more democratic. In fact they made it more centralized and self-serving for the leadership. That the unions were somehow to blame when in truth they were never that far to the left. And lastly that it needed this move to the right to be able to take on Tories and win. The truth was that the Tories beat themselves in the end with internal fighting and sleaze.
Were the Militant Tendency to blame? Partly, as they gave Kinnock and company the target to destroy the CLP's power. As revolutionary socialists they saw nothing wrong with the strategy they used, but in hindsight all they did was open door to the right. Probably the most important lesson to be learnt was that most Labour MPs were, and are now, there for things other than socialist principles. Britain's main socialist party was and is represented in parliament by people who were not socialist in the slightest.