No university in the UK has a "paper requirement" that I'm aware of. You're encouraged to publish, but it's not mandatory. Published work does increase the odds of successfully completing the process, because it pre-vets the work, but I've known people to finish with only one paper (or even zero). I'm writing up my thesis now, and have only 1 paper (a workshop, so really only 1/2). I hope that most of my work will be published post-thesis.

Of course, UK PhDs are very different to the US - here, 3 years is a normal timescale to completion, and 4 years is the maximum my department allows. Frankly, in any "deep" subject, that's barely enough time to work out what the state of the art is, let alone advance it.