u/howtoeatflextape

My Reasoning:

Sherlock yack first aired in france on May 4th 2011, with the date of June 18th most likely being international releases.

The show aired once a week in blocks of two back-to-back episodes

Given this information, episode 4: "who tagged the bird of paradise?", in which it was hermione's birthday, first premiered on May 11th.

Which means her birthday is most likely:

May 11th.

Everyone should wish my stoat wife a happy birthday