By literal definition? None.
In effect? Quite a lot.
The PM does effectively have the power of the crown at their disposal and may implement specific actions under the Royal Prerogative. Officially, these are actions enacted by the monarch on the advice of the PM, but (as recently occurred with the prorogation), the Queen follows the government's advice without public comment on the matter.
However, the extent of the Royal Prerogative is hazy to say the least.
The prerogative appears to be historically and as a matter of fact nothing else than the residue of discretionary or arbitrary authority which at any given time is legally left in the hands of the crown. The prerogative is the name of the remaining portion of the Crown's original authority ... Every act which the executive government can lawfully do without the authority of an Act of Parliament is done in virtue of the prerogative.
~ A.V. Dicey, 19th Century constitutional theorist
Any actions taken by the PM using this authority are subject to appeal in the courts and it is the judiciary who would be the final arbiters post facto. Parliament, however, remains supreme and they could countermand any executive actions by the Prime Minister (provided they are sitting and parliamentary process allows).
In terms of what actions are taken via Royal Prerogative; Pardons, Declarations of War or Peace, Dissolution of Parliament, Signing of Treaties, and (ironically) appointing the Prime Minister, are the most commonly used. The majority of times these are enacted is done with the prior approval of Parliament.
There was the suggestion in 2017 that Theresa May may use the Royal Prerogative to issue the notification of Article 50 (the start of the United Kingdom's departure from the European Union), however it was decided in court that the power to do so resided with Parliament not with the Crown.