How many new words in Shakespeare?

Estimates of the number of new words and phrases used in the complete work of William Shakespeare vary considerably. 

In 1942, leading Shakespeare scholar Alfred Hart, wrote that the Stratford playwright is "credited by the compilers of the Oxford English Dictionary with being the first user of about 3,200 words." 

That number is now considered an overestimate. But by how much?

A British Council website from 2016 suggests 'more than two thousand' while the invaluable Online Shakespeare Biography goes with around 1200.

Linguistics Professor Jonathan Culpeper and his team at the University of Lancaster has produced a new dictionary based computer analysis of the full corpus of the Bard. 

He suggests a much lower figure, "somewhere in the order of 400". This is still an astounding number for a single author. As Culpeper points out  "modern writers are lucky if they’ve invented one word."