Who ranks second in a British government?

Who ranks second behind the British prime minister?

The First Secretary role is the constitutional number two described here, but a separately appointed deputy prime minister may complicate the hierarchy.

Britain does not always give one office a simple, permanent claim to rank second after the prime minister. The First Secretary role is described as the constitutional number two, while a government may also appoint a deputy prime minister. Those titles can be held by different people. The hierarchy therefore depends on the offices and appointments in force at the time.