Are U.K. grade cutoffs for PhDs hard? I recently learned that most U.K. universities advertise themselves as having a minimum grade cutoff of a 2:1. I’m an American, and according to Cambridge’s website, they consider a US 3.5 to be the equivalent of a 2:1.

I did some google searching, and on College Confidential people seemed to think that that is a hard cutoff, and your application won’t be looked at if you’re below a 2:1. This really surprised me because, in the US, failing to get a 3.5 is detrimental, but by no means the end of the world, for PhD applicants. I’ve seen plenty of schools advertise a 3.0 cutoff.

Is a 2:1 a hard cutoff for U.K. PhD applicants? Is a 3.5 a hard cutoff for Americans who want to do PhDs in the U.K.? If you do a masters before your PhD, does this apply to the masters coursework?
With the caveat that I don't speak for my department or institution (although my experience informs my opinion):

My inclination is to say that in practice the cutoff can be softer than the official advertisements or instructions, but this isn't guaranteed, and may even vary between departments at the same university.

The cut-off is usually there as a first-pass filter for applicants who got their Bachelor's or Master's degree at a UK university. Conversion of grades from other systems, such as US GPA, is done according to some University-determined scale, but depending on the volume of applications at any given university there may be scope for some ad hoc decisions on edge cases.

It's also the case that the relevant admissions committee/team will probably look at the awarding institution, even if GPA is supposed to be standard. A 3.4 from an institution which is known to have a strong undergraduate program, or which has a positive reputation among the academics reading the application, will get treated more favourably than a 3.4 from somewhere that is "less esteemed" in some sense.

(I think one reason the cut-off is higher in the UK is because our PhD programmes are usually shorter than the US and have a less comprehensive training period in the initial stages - so we need to get people in who are better prepared, rather than take a risk on someone with patchy background but some signs of potential. But this is just my experience/opinion from mathematics, and it could be way off-base for other disciplines.)

Even within the UK it's not clear to me that the cutoff is as strict as official statements imply. To take a not entirely hypothetical scenario: an institution might say applicants in mathematics should have a 1st class degree or equivalent. Yet if they get an applicant who has a 2:1 Bachelor's from, erm, certain UK institutions, with good references and with some positive predictions about the Master's program on which they are currently involved... I think that such an applicant has a decent chance of being considered seriously by the departmental admissions team, provided that the application material has made it through the centralized university pipeline.