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20-year-old Brundle, previously at Yeovil Town and Bristol City, has been at Cressing Road since signing for the club last summer, and will take up a role within the club's Academy coaching team.
23-year-old Habergham was a trainee at Norwich City, and has played over 120 games for the Iron.
Earlier during the summer, Braintree announced that they had signed Concord Rangers centre-back Matthew Fry, who has had professional experience at West Ham Utd, Gillingham and Bradford City.
Friendly News: Braintree Town will send an X1 side to Stanway Rovers, on the new date of Saturday 18th July (3pm).