Seems plausible, though I still think the US threatening to do that, let alone actually doing that, is more likely to cause a separation between the US and UK than to be taken seriously (in the sense of getting the UK to change course).

The UK did just go through having Boris Johnson as Prime Minister, after all, who spent his time in office demonstrating that being completely shameless is a viable solution to almost all blackmail — he only fell when there were photos of him partying in the same period he was on TV telling people they couldn't do that or visit dying relatives because COVID lockdown, everything else wrong was basically ignored.