A U.K. investment firm is paying about $400 million to acquire Freehand Hotels, the New York-based lodging company majority owned by hotel operator Sydell Group and private-equity investor Ronald Burkle’s firm.

Queensgate Investments LLP, the U.K. private-equity firm acquiring Freehand, plans to operate the U.S. company alongside its Generator brand, which manages 13 European hotels and hostels in Rome, Paris, Venice and other major cities. Generator recently opened its first U.S. properties in Miami Beach and Washington,...