Exact process is P.M. submits a list to Palace for approval, like every other matter of government she just rubber stamps it, the nominee then receives a letter from the palace along the lines of "we are minded to award you....whatever award....if we were to award you ....would you accept. Etc.” If the nominee says that they do not wish to receive it then no more is said .
Having been involved in the collation of supporting information for such an honour, I can tell you that the honour was applied for. The honour can be applied for by the person themselves or by someone else.
It is much more than submitting a nomination to a government group who then suggest it. The supporting information needs to be quite substantive and for the best results you should have a Lord as part of the supporting cast. Someone from a governing body helps too. Easy when nominating Dalglish or the likes. Not so much so when nominating a nurse or head teacher.