Kiss' success is a significant moment for Emap Radio, which also owns Magic, meaning it is behind two of the top three London stations.
Magic, which came top in the survey last quarter, increased its share from 5.9% to 6.2% and its reach from 1.81m to 1.96m.
However, Global Radio's Heart grew its share from 5.4% to 6.2% and its reach from 1.7m to 1.81m, reeling in its rival.
Both stations overtook the BBC's Radio 1 -- its share fell from 6.7% to 5.5%.
Magic has the edge on reach, but Heart can also claim to have the most-listened to breakfast show, with 874,000 listeners to Magic's 823,000. Last quarter, the equivalent figures were 825,000 for Heart's Jamie and Harriet and 721,000 for Magic's Neil Fox.
Capital's Johnny Vaughan breakfast show lost 18,000 listeners, dropping from 854,000 to 836,000. Vaughan first lost the top spot to Theakston in the fourth quarter of 2006, before regaining it last quarter.
At a station level, Capital's share of listening fell from 4.6% to 4.1%, while Kiss's share increased from 3.9% to 4.5%. Capital's reach is down from 1.62m to 1.52m, while Kiss's is up from 1.36m to 1.52m. The swing may be reversed in the next survey, but it is a worry for investors in the UK's biggest commercial radio company that it no longer has a station in London's top three.
Fru Hazlitt, GCap's managing director of London stations, speaking to Brand Republic this morning defended Capital, saying GCap believes the station can get its former number one position back.
She noted the station grew its share of 15- to 34-year-old listeners and shed those from older age groups, in line with its strategy of repositioning itself as a contemporary music station.
Outside the top four, Virgin Radio recorded the next highest share at 3.3%, up from 3.2%. Its reach was up from 1.13m to 1.16m, a decent performance as it prepares for a separate stockmarket listing to parent company SMG in the autumn.
Global Radio's speech station LBC is on an upward trend, with its share rising from 3% to 3.1% and its reach up from 597,000 to 637,000.
GCap's Xfm recorded a share of 2%, up from 1.8%, but its reach fell 13,000 to 617,000.
Following its relaunch in March as an easy listening station, GMG Radio's Smooth Radio London's share dropped from 1.7% to 1.4% although its reach grew from 473,000 to 502,000.