Tony Blair (remember him?) was long accused of a "presidential" style of government. His ministers were completely under his authority, and always replaceable. This may be part of Gordon Brown's problem - he is attempting to govern in Blair's style, and running out of MPs who can complete his cabinet. The problem is that Blair had three things enabling his presidential government, which Brown doesn't have:
1. The authority with the party that came from being a proven election winner
2. People skills
3. Gordon Brown
Number 3 is the punchline, of course; but the Blair regime was a double act from beginning to end. No other minister had the power to overrule the prime minister.
The real point was that the sidelining of the cabinet under Blair was not so much part of the general centralising trend as an aspect of Blair's particular personality and situation.