Tories saw a big swing to Labour in a by-election for their flagship Wandsworth Council.
The majority was slashed in Thamesfield, Putney - in contrast to earlier trends in other Conservative strongholds.
This was despite the public sector strike action which might have been expected to bolster Tory support in such an area.
The party's slump in Wandsworth was mirrored in the the only other contest at Cheshunt Central, Broxbourne Borough, Hertfordshire.
The Wandsworth by-election is the borough's first for 12 years, the previous such contest being in the last century.
It was caused by the resignation of former council leader Edward Lister after his appointment as chief of staff to London Mayor Boris Johnson.
Analysis of 24 comparable results in June suggests a 1.4% projected nationwide Labour lead over Tories.
A calculation based on 11 wards fought both times by all three major parties gives a line-up of Labour 38.2%, C 38.1%, Lib Dem 13.7%.
The calculations of projected party leads and vote shares are based on general election figures for wards last fought in 2010.
The basis for seats previously contested in other years is statistics published by the BBC after main council polls. These have tended to be close to other published surveys.
Broxbourne Borough - Cheshunt Central: C 742, Lab 481, Ukip 88, Ind 62, Lib Dem 24. (May 2011 - C 1175, Lab 495, Ind 206). C hold. Swing 8.7% C to Lab.
Wandsworth London Borough - Thamesfield: C 1497, Lab 1022, Lib Dem 545, Green 202. (May 2010 - Three seats C 4938, 4685, 4654, Lab 1559, 1387, Lib Dem 1479, 1194, Lab 1192, Lib Dem 1043, Green 849). C hold. Swing 13.2% C to Lab.