You can set up a Limited Company in about 5 minutes over the internet if you know what you are doing.
The minimum number of shareholders is ONE. And indeed most newly formed companies only have one share initially unless they choose to issue more.
Since October 2009 companies haven't needed a Company Secretary, though they can have one if they so wish. And a Company Secretary can indeed be a shareholder. They can also be the same person as a sole director now though again that's only since October 2009.