Full Idea
For Mill the greatest happiness will be achieved by giving people a private sphere of interests where no intervention is permitted, while allowing a public sphere where intervention is possible, but only on utilitarian grounds.
Gist of Idea
Maximise happiness by an area of strict privacy, and an area of utilitarian interventions
Source
report of John Stuart Mill (On Liberty [1857]) by Jonathan Wolff - An Introduction to Political Philosophy (Rev) 4 'Liberty'
Book Reference
Wolff,Jonathan: 'An Introduction to Political Philosophy (Rev)' [OUP 2006], p.119
A Reaction
This is probably standard liberal practice nowadays. Freely consenting adult sexual activity is agreed to be wholly private. At least some lip-service is paid to increasing happiness when government intervenes.