The cabinet is the senior decision-making body in government. As described by the Cabinet Manual, the cabinet is "the ultimate arbiter of all government policy" and "decisions made at cabinet and cabinet committee level are binding on all members of the government."
Be it a Labour, or Tory government the PM is simply "first amongst equals" and he or she dosent have to be at all COBR meetings ,very frequently a senior cabinet minister with a specific role to the purpose of the meeting will chair it.
The cabinet is typically chaired by the prime minister and comprises the most senior ministers in government. Formally it is the cabinet that governs the UK – although the role of the prime minister within the cabinet gives him or her particular powers over the decisions made by the cabinet.
The term ‘cabinet’ also refers to the meetings of the cabinet, as well as the body itself.