Apple and Google did not know the UK government planned to build a “hybrid model” bringing their contact-tracing system together with the NHS app until Matt Hancock promised to do so on television.

While the California companies knew the UK was about to change course and begin using their tech, senior figures had no idea that the health secretary would claim that there were problems with their system in determining how far apart phones were. They also did not know that app chief Dido Harding would claim to have “developed new distance technology that will enhance the Apple/Google version”.

In a statement, a Department of Health and Social Care spokesperson said: “NHSX [the health service’s technology unit] has been working with Google and Apple extensively … There is a commitment between the teams to work together to improve the distance measurement technology, which is integral to have a fully functioning contact-tracing app.”

That new distance technology would be the only material outcome of the more than £11m spent on the first version of the app, according to government contacts with the companies contracted to build it. More than half that money, £6.5m, went to German consultancy Zuhlke Engineering, which was also involved in building the second version of the app.

“Our response to this virus has and will continue to be as part of an international effort,” said Harding, the head of NHS test and trace, and Matthew Gould, CEO of NHSX, on Thursday.

“That is why as part of a collaborative approach we have agreed to share our own innovative work on estimating distance between app users with Google and Apple, work that we hope will benefit others, while using their solution to address some of the specific technical challenges identified through our rigorous testing.”

The suggestion that the system doesn’t work well enough to use nationwide caused particular confusion. Apple told the Times: “It is difficult to understand what these claims are as they haven’t spoken to us.” The same system is already in use in Germany and Italy. “There have been loads of field tests by public health authorities that have shown it works effectively,” one person involved with the project said.

The leader of Germany’s app team, SAP chief technology officer Jürgen Müller, told reporters on Tuesday that “in the last test series, we were able to correctly estimate around 80% of the encounters”. That error rate, of around 20%, is “more than justifiable”, the federal minister of health, Jens Spahn, said, according to German news site Golem. “It is better to test too much than too little.”

But the UK government believes that it can reduce the error rate if it can convince the Apple/Google team to loosen one restriction in the tools they make available.

Currently, Britain’s developers are struggling to consistently use the tools to distinguish between contacts at a 1 metre distance, which ought to trigger self-isolation under government guidelines, and contacts at a 3 metre distance, which ought not trigger a warning.

The problem lies in variations between different models of mobile phone, which send out the Bluetooth signals used for the tracking at slightly different strengths. In the original NHS app, the make and model of phone was included in the system, allowing the app to alter its estimates accordingly.

But the Apple-Google system doesn’t allow that information to be sent out as part of the tracking system, in order to prevent users from being tracked by malicious actors, according to a person with knowledge of the system. “Any change that affects an entire operating system’s security and privacy properties will be really hard to get through Apple and Google organisationally,” the person said.

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