The UK is required by the terms of the treaty to decline extradition on that basis. From the treaty,[1]
> extradition shall not be granted if the competent authority of the Requested State determines that the request was politically motivated.
There's no doubt about the political nature of the prosecution, so there's no doubt about what the outcome should be, unless there are extra-legal considerations at play in the decision. We're all watching the answer to the following question be played out in real time: "Will the UK extradite a person for politically motivated prosecution in the US, in flagrant violation of the UK-US extradition treaty?"
1. https://assets.publishing.service.gov.uk/government/uploads/...