Despite heavy advertising support, Vaughan is not expected to top the 1.37 million listeners that tuned into Chris Tarrant's breakfast show in the first quarter.
Helen Keable, the head of radio at Manning Gottlieb OMD, said: "I think the best that Capital can hope for is the figure to hold; listening staying level would be a very good result for it."
Tim McCabe, the head of radio at Vizeum, said: "I predict a 20 per cent drop for Vaughan but that might not be as bad as it sounds because I think his audience leans towards a young male bias."
Rajar figures for the second quarter, which include the final two weeks of Tarrant's show, will be the first official indications of Vaughan's popularity following his move to the station in April.
Strong competition from Virgin, Heart and Radio 1's Chris Moyles following Tarrant's departure is said to have led to unusually high churn in London audiences.
However, Capital sources said they were happy with Vaughan and indicated that they were taking a long-term view of his audience.
Keith Pringle, the managing director of Capital FM, recently hit out at criticism of Vaughan that suggested he was alienating the female element of Tarrant's audience, claiming that "among women from the age of 20 to 45, he is doing a very good job".