The 50-year-old is believed to be leaving for personal reasons after a City career spanning 23 years.
Melling became Cenkos’ chief executive two years ago after serving as its chief operating officer and finance director since its listing on London’s AIM in 2006.
He moved up to head Cenkos in 2009 to allow its founder, racehorse owner Andrew Stewart, to step back from day-to-day running after his son was paralysed from the waist down in a snowboarding accident.
No successor for Melling was announced, suggesting no internal candidate had been selected, and he will continue in post for the next three months until one is recruited. The news surprised the market, sending Cenkos shares down 8.7 per cent.
Cenkos chairman Peter Sullivan said the board “will be sorry to see him move on and he will leave with our best wishes”.
“His commitment has been a driving force since day one and we are very grateful for all that he has done,” he added.