It coincides with news of a similar flaw discovered by two US researchers.
However, NCC's work - which has been restricted to its labs - points to a wider problem.
NCC demonstrated its technique to BBC Radio 4's PM programme at its offices in Cheltenham.
Because infotainment systems processed DAB data to display text and pictures on car dashboard screens, he said, an attacker could send code that would let them take over the system.
Depending on the power of the transmitter, he said, a DAB broadcast could allow attackers to affect many cars at once.
"[An attacker] would probably choose a common radio station to broadcast over the top of to make sure they reached the maximum number of target vehicles."
Mr Davis declined to publicly identify which specific infotainment systems he had hacked, at this point.
Mike Parris, of SBD, another company that specialises in vehicle security, said modern cars typically contained 50 interlinked computers running more than 50 million lines of code.
By contrast, he said, a modern airliner "has around 14 million lines of code".
Such technology allows the latest cars to carry out automatic manoeuvres. For example, a driver can make their vehicle parallel park at the touch of a button.
"If someone were able to compromise the infotainment system, because of the architecture of its vehicle network, they would in some cases be able to disable the automatic braking functionality," he said.
"So, it sounds entirely plausible."
But he added that such exploits were beyond the reach of most criminals.
"It takes a lot of time skill and money," he said.
More details about both the NCC and the US team's research will be presented to the Black Hat security convention in Las Vegas next month.