>>12582331The research councils have changed since I went through the system. As I understand Engineering PhDs are typically funded by the research council, in this case EPSRC. It seems that they do offer places for international students, but there's less places for them than UK resident students.
https://www.findaphd.com/funding/guides/epsrc-funding.aspxWhen I applied I didn't actually do any of the funding myself, the department will pick who they like and then worry about money. You could contract the departments (or specific groups) to see if they are aware of other funding that you may have to specifically apply for or staff who have existing grants and are looking to hire.
Note these are often called studentships rather than scholarships. If it is funded that means you will get a stipend.