British English equivalent of American English "kitchen cabinet", where the head of government (PM or President) makes key decisions with an unofficial advisory group (metaphorically "around the kitchen table" or "sitting on the sofa in the den")
Usage: The PM relies on sofa government to make key decisions, while his friend the President goes straight to his kitchen cabinet.
decision-making by a small group of advisers with common interest or purpose
Usage: The sofa government style made the rest of the cabinet members angry because none of them were consulted about the introduced policies.
Sofa is an item of furniture used for a relaxed conversation, discussion or watching television or having cocktails. Sofa is not fit for serious reading or writing or for that matter any serious work or business. Hence a sofa government would be one that has gone soft and does its business of governance in a non-serious way.