Hi Yandex,
Offers can take a while to go through the bureaucracy, I would give it at least two weeks.
I had about 3 weeks between being confirmed verbally and actually getting an official offer via email. They will have to do a lot of bureaucratic stuff like check eligible for the bursary, check references (if they are), check if you actually achieved the actual grades, put all of the above onto the IT system before having someone review over it all. Each step could also be done by different people also dragging it out, so don't be worried.
If the supervisor wanst you, there is a very good chance you will get it an official offer but some things can't be rushed. Though I don't know University is Salford procedures so there could be more to it.
Hope that helps and congrats on passing that interview!