The news will be a boost to Radio 1 and to Cox, who suffered in the latest set of Rajars for the April to June period when the 'Breakfast Show' lost 433,000 listeners, while Radio 1 audience figures slipped under the 10m mark to 9.9m from 10.5m last time.
GFK's figures show that the BBC's national youth offering is the most popular station among adults aged 16-44 years old, with 40% of this age group's weekly reach, for the period between April 21 and July 20.
GFK Media director Nick North said: "Looking at the performance of the 'Breakfast Show' among the core audience of 16- to 44-year-olds, using Radiocontrol's electronic audience measurement system, we're seeing a steady improvement during the past three months, with significant growth of the average daily audience. On this evidence, Ms Cox should be pressing for a pay rise, not fighting for her future."
The research, which is backed by Kelvin MacKenzie's The Wireless Group, also shows that its radio station TalkSport is the UK's leading commercial station with 7.2m listeners and a weekly reach of 16%.
The system uses electronic measurement of user's listening habits, as opposed to Rajar's methods where diaries are kept. GFK and TalkSport owner The Wireless Group's chief executive Kelvin MacKenzie believes the electronic system is more accurate. This is disputed by Rajar, which has conducted its own electronic technology trials.
However, some things do not change. Radio 1 still loses its number one spot when the figures for over-45s are added, and falls back behind sister stations Radio 2 and Radio 4, as in the Rajar figures.
According to GFK, Radio 4 has a weekly reach of 40% and 18m listeners; Radio 2 has a reach of 35% and 15.7m listeners; and Radio 1 has a share of 28% and 12.6m listeners.
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