A competitive pitch is being overseen by Matthew Grossman, Disney EMEA's vice-president of corporate comms, publicity and corporate citizenship, and the winning agency is expected to be picked by March.
The brief extends to working on Disneyland Paris as a destination for UK families, alongside its UK entertainment properties.
The latter include its TV channels The Disney Channel, Disney Junior and Disney XD; its children's social network Club Penguin and its movie arm Walt Disney Pictures.
It also runs live shows based on its properties, such as The Lion King, and operates a small number of Disney stores.
Disney bought Star Wars producer LucasFilm in 2012 and it was announced last year that the new Star Wars movie would be made in the UK, as were previous films in the series.
Disney currently handles all of its corporate and public affairs work in-house.