Very few. The only one I am immediately aware of is the selection of members of the Order of the Garter: the highest order of honour in the UK honours system, and so part of the system of the state. This remains in the personal gift of the Monarch.
This hasn't always been the case, and from the 18th century, nominations were made on the advice of ministers. Clement Atlee restored to the king the power to create Knight Companions of the Order of the Garter without consultation with the government in 1946.
The Order of Merit (founded in 1902) similarly is in the personal gift of the Royal Household (ie the Queen and her non-ministerial advisers)
In extreme circumstances, the reserve powers exist. But they exist when the government is acting extraconstitutionally. The reserve powers are not part of the constitutional system of government. Thus the armed services swear allegiance to the Queen. If a Prime Minister were to declare themself to be a dictator, the Queen could order the army to depose them. But clearly neither a dictatorship nor the military coup is constitutional.
In nearly all other actions of the state, the queen acts on advice. The current monarch has repeately shown no desire to be involved in a political decision.