Councillor Barrett was the leader of the Upminster and Cranham Residents' Group and had been a councillor for 12 years, after being voted in in 2006.
He was also cabinet member for finance in the previous administration between 2014 and 2018.
The poll is set to take place on Thursday, May 9, and the deadline for voter registration is Thursday (April 18).
Deadline for postal vote applications is 5pm on Tuesday, April 23.
Linda Joy Van den Hende - Upminster and Cranham Residents Association.
For more information about the by-election go to Havering Council's website.