Many generalist predators, including fish, insects and mammals, temporarily focus on their search behaviour and can switch between prey species. Flexible and rapid behavioural plasticity enables a predator to forage optimally, as guided by search image formation and prey switching in response to changing prey abundances. More than half a century of studies have used Holling type III functional response to model the impact of this feeding behaviour on population dynamics, yet a mechanistic understanding for the pathway between individual behaviour and feeding rates remains poorly understood. To understand this common feeding behaviour, we developed three mechanistic models using first-principles to provide direct derivations for the relationship between observed individual behaviour and feeding rates. The derived models yield three novel, generalised functional responses for predators characterised by prey switching and mutually exclusive feeding (i.e. feeding is limited to one prey species at a time). We show how these functional responses act as Holling type III response, and how they can be used to predict predators' diet compositions. Our results demonstrate that several behavioural forms of prey switching, as displayed in a wide range of predator species, consistently produce type III conforming functional responses.