Well, it's not really New England accents, but it sounds more of a mixture of the "West country" accent (i.e. Cornwall, Devon, Somerset, and Dorset), and the Coastal Southern accent in the US. One of the main ways we know that is the rhyme schemes in the plays and poetry. In the modern "received pronunciation" they don't rhyme. However in what people call the "original pronunciation" they do. The accents of the time were also known to pronounce words more like they were spelled. i.e. film being phil-om. Also there are some accounts of how words were pronounced at the time.

A helpful video about original pronunciation.

[NPR article about how they developed OP.] (http://www.npr.org/blogs/monkeysee/2012/03/24/149160526/shakespeares-accent-how-did-the-bard-really-sound)

Also here you can listen to some samples of Shakespeare in OP.