Prime Minister

If a Prime Minister was deposed, would it be possible for she or he to again be elected to the post if they had enough popular and/or party support?  Rather, how would a Prime Minister who was essentially forced to resign get the post back?   Could they do it legally?

Thanks for your help.

ETA: This entry is specifically based upon Harriet Jones, who was "deposed" by the Doctor.  Under what circumstances could she get back into power?