The Shakespeare is a pub. Mitchell, Annie and George go there when they go out together for the first time. Their friendschip has become stronger and even George begins to like Annie. There they are like completely normal people, who talk among other things, about the houses they would choose of the Harry Potter books. George would like to chose Ravenclaw, Annie Slytherine and Mitchell just wants to stay in the cantine.
The Shakespeare is also mentioned in the book The Road. George and Mitchell go there together with the journalist Gavin Foot. Furthermore it's mentioned, that Annie, George and Mitchell often go there in their freetime. They even have a favourite table (the one that they were sitting at in the Pilot Episode).
The Shakespear is called The Oxford. It is near Annie's house.
120-122 Oxford Street