As a non-American: Where exactly do you think justice isn't political? Justice can be more or less blatantly tied to the party politics of a country, but it's always political. Laws aren't handed down from the heavens and aren't enforced without regards to who has the power to change the laws.
Our prime minister doesn’t have the power to pardon convicted criminals. He can’t just sack or appoint judges. And new laws have to be scrutinised by both Houses of Parliament before being passed.
So how is it much better to leave the power of the pardon to the Secretary of State for Justice, who's appointed by the Monarch on the advice of the Prime Minister? Sure, the US situation is more fucked up. But that sort of power is always political, even if it's not democratically elected.