Yes, I'm pretty sure you'll find a list of universities that are part of a scheme on the relevant research council website (eg ESRC, AHRC etc).
I think you are expected to stay at the same university for the whole thing, although in certain circumstances you can definitely switch and take your funding with you. I am just not sure if it is something that is allowed in the sense that it is part of the plan (as opposed to circumstances changing and you wishing to move).