Two big differences between US and UK PhD programs are that full time UK programs are designed to be 3 years (with a pretty hard limit at 4 years) and many students, even in engineering and science, are not funded.
Admissions to UK PhD programs, even the top programs, is significantly easier than in the US. Ignoring funding for a moment, admissions in the UK is almost entirely dependent on finding a willing supervisor, while in the US having a supervisor is not generally enough to gain admissions. So if you can find a supervisor who is willing to take you on as a part time PhD student, your chances of getting in are pretty good.
Funding is a whole different story. Externally funded studentships in the UK are generally for full time students and departments generally do not like to commit themselves to 6 years. That said, tuition and fees in the UK can be much cheaper and self funding a UK PhD is much more common.
In terms of finishing, I think a part time student in the UK has advantages that part time students in the US do not. Full time students in the UK lose their funding after 3 years and must be finished by 4 years while part time students have at least 6 years to finish. As some aspects of the PhD cannot be rushed, there are times were working less for longer is a definite advantage.