In the late 1960s the Swifts moved to their own ground on the outskirts of Heybridge, at Scraley Road. After winning the Essex Senior League for 3 seasons running the club were offered a place in the Isthmian League, which had just added a new division by splitting its Division 2 into 2 regional leagues. Since then the Swifts have gradually progressed to reach the Premier Division of the Isthmian league (now sponsored by Ryman) - just one step down from the Football Conference, England's national semi-professional league.
Heybridge Swifts achievements have come without them spending vast sums of money to attract the best players - a trend that has seen other clubs struggle financially, and in some cases fold completely. Heybridge recently decided against accepting the benefaction of a celebrity millionaire, preferring to keep the club as a friendly family club with realistic expectations.
Heybridge have still managed to reach the 1st Round of the FA Cup on 2 memorable occasions, losing 2-0 to Gillingham and 3-0 to Bournemouth respectively. Players who began their career with the Swifts have gone on to Football League clubs - the best known being Simon Royce who has appeared in the Premiership with Charlton Athletic.
The Swifts official nickname is simply 'The Swifts' or the 'Black and Whites' but to hard-core, dyed in the wool Swifts supporters the cry is 'Come on you Carrot Crunchers'.