Disney Life will feature many of the company's films, music, books and television programmes in a single app.
However films from its Star Wars and Marvel franchises will be absent at launch.
The service will mount a challenge to rival services like Amazon Prime Video, Netflix and Now TV.
One analyst said content creators were beginning to compete with the traditional pay TV companies on whom they previously relied.
"Content companies like HBO and Disney are realising that old business models no longer make sense," said Mark Mulligan from technology analysis company Midia Research.
"They used to sell their programmes to pay TV providers. Now, in the digital era, they can have a direct relationship with the consumer.
"Kids' TV is often a lower priority for pay TV providers because the bills are paid by adults who are more interested in movies and sport.  This is Disney saying 'We think we can do it better'."
Disney said its new service would give families instant access to hundreds of its films, songs and books for a monthly fee of Â£9.99.
It will be more expensive than rival services by Amazon and Netflix which have films from a variety of providers in their libraries, but less costly than subscribing to its cable and satellite channels.
Disney told the BBC its new service would "co-exist" with existing streaming services and was launching in the UK because of its "many Disney fans".
"UK families embrace new technology, and demand more flexible entertainment, and this is supported by superfast broadband connectivity and the proliferation of digital devices in this market," a spokeswoman said.
An increasing number of programme-makers are launching their own video apps, known as "over-the-top" services because they bypass traditional pay TV providers and offer a subscription to anybody with an internet connection.
"Inevitably, people who want to pay for video are going to face a fragmented landscape," said Mr Mulligan.
"It's not just about monthly subscriptions. You may end up locked into a service with proprietary hardware.
"Hopefully in the future a company will be able to bring all the content back together in one service."
Disney is to launch its own subscription-based video streaming service in the UK.