Russell Group scientist here who is responsible for PhD training and scholarships in my department.
It doesn't matter a huge deal if it is a taught masters or a MRes, although we slightly prefer taught masters. We do expect excellent grades at bachelors and masters - at least 2.1 & merit, but to get PhD funding a first and distinction are helpful, or at least one of them. A masters from a top uni is always going to be a much better entry ticket than a masters from an ex-poly. I hate the system but a 2.1 from a Russell Group uni would be considered better than a first from a low-ranking one.
A research-active masters dissertation supervisor who works in the field of the intended PhD would be good, as it can be possible to attach to other research projects they do and get funding that way.
There are also a lot of 'soft criteria' that help with PhD scholarships: being able to demonstrate determination/perseverance/leadership/enthusiasm, e.g. Student union activities, in sports clubs, volunteer work, in summer jobs or wherever. Going the extra mile and having 'studied widely', for example doing extra voluntary things such as helping organise a conference, internship, attending departmental seminar series, taking an extra optional module...
I read a lot of PhD scholarship applications, and ideal candidates are excellent academically, passionate about the subject, have a god idea what they would like to do during their PhD and beyond, and have shown they can work on a project and make a success of it.
Good luck! Not an easy career but very rewarding.