Blocking the extradition would be very simple. The extradition request shouldn't trouble the courts for long since in this case there's nothing complex or unusual to decide, so it's no more than a matter of checking the paperwork. The UK's current extradition treaty with the US is 20 years old, so both sides understand each other's requirements. Extradition from ECHR countries, such as the UK, to the US is more complicated than from the US to the UK because the US legal and penal systems have all sorts of human rights issues, as we saw with the Assange case, and we sometimes also refuse on health or dual criminality grounds (i.e. the conduct alleged on the indictment doesn't amount to a criminal offence in the UK).
There's no question about whether the treaty covers the alleged offences or whether the Tate brothers currently in custody are the same men named in the indictment. The Crown Prosecution Service's test (is the evidence sufficient for a reasonable jury, properly instructed about the law in the case, to convict, if they accept the prosecution case?) meets the US test of probable cause, and there's no external exculpatory evidence available (the brothers were not, for example, in custody at the time of the alleged offences).
The credibility of the prosecution case is a matter for the English court and jury, not the US court, as is the Tate brother's defence.
However, once the court approves the request, it must then also be approved by the Secretary of State, currently Marco Rubio. His decision is final. So if Trump wants to block it, he simply has to make his wish known to Rubio, who (at least on present form) will presumably meekly agree. End of story.
However, the current extradition treaty was signed in 2003. Since then, the US Secretary of State has approved 87 British requests and refused only one, that in the case of Anne Sacoolas, whom the UK wanted to try for causing
the death of Harry Dunn by dangerous driving, and, at least at present, the White House and Rubio have both indicated they don't intend to intervene on behalf of the Tates.
Social media influencers to be extradited after UK authorities file dozens of new sex crime charges against them.
www.aljazeera.com
That can change, of course, but I suspect that Trump and his advisors are reasoning that the Tates' supporters will soon forgive him for handing them over to the British criminal justice system (he probably believes, with reason, he could stand in the middle of Fifth Avenue and shoot both brothers without losing any of his hardline MAGA fanatics) and that the last thing he needs right now is to stir up a domestic and international controversy about protecting yet more alleged prolific rapists, sex traffickers and creators of CSAM who aren't even connected to Jeffrey Epstein.