It is the latest sign of easing tensions between public service broadcasters, as rapid changes in viewing habits force them to abandon old rivalries to survive.
The broadcasting watchdog Ofcom has said "audiences could benefit significantly" if the broadcasters' shows were offered through a combined service that was widely available when it published a review last month.
The BBC, ITV and Channel 4 already collaborate on Britbox, a subscription streaming service focused on classic series. An industry source insisted plans for an all-in-one British television app will not diminish the need for new laws to underpin public service broadcasters' claim on the homescreen.
Traditional television regulations hand them the highest spots on channel menus in exchange for making news and public services programmes that tend to attract smaller audiences.
However, there are fears public service shows will struggle to reach audiences in the future as younger viewers switch their allegiance to American streaming platforms, while current laws give no guaranteed position on smart TVs and connected devices.
Research by Ofcom in December found that 43pc of viewers using on-demand streaming services can imagine watching no broadcast TV in five years' time.
It comes as the TV mast monopoly Arqiva is poised to pull out of the TV platform YouView, a joint venture with the BBC, ITV, Channel 4, Channel 5, BT and TalkTalk.
It follows the infrastructure giant's decision in December to step down as a shareholder in Freeview, the main terrestrial broadcasting platform.
The Sunday Telegraph revealed in October that Arqiva had refused to help fund a new Freeview streaming service because it would not rely on traditional broadcasting infrastructure.