I saw the organiser of the Walthamstow Wassailers and she is not aware of any Essex specific wassails.
Somone I haven't seen for a few years but used to be a regular drop in at the club is Tony Kendall "The Essex Man". Here is a link to a website which gives more info and refers to Essex Wassails but Tony not only collected but wrote "folk" related songs on Essex themes so they may be his own work.
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sj