The agency has launched with first client Corlytics, a company that provides software that measures regulatory compliance.
Leighton, who left Hudson Sandler in September last year, has held a number of senior roles in PR across more than 20 years at companies including Edelman, Text 100, Waggener Edstrom and Orange.
Leighton said the agency specialised in "enriching messaging".
She said: "I’ve spent many a year fantasising about setting up my own agency. One where people come first. Where passion and creativity are prized. Where clients are celebrated. One where there is time to think, to go the extra mile. A land of opportunity, hence Milk & Honey."
Leighton worked at Hudson Sandler for more than five years. Last year Huntsworth sold its majority stake in the agency as it became a limited liability partnership. Milk & Honey is also an LLP.