The party is predicted to fare better - and might even gain a few seats - in the Metropolitanboroughs, where it currently controls 16 of the 36 councils.
It is claimed two county councils - Lancashire and North Yorkshire - and six metropolitanboroughs - Calderdale, Doncaster, Ealing, Kirklees, Rotherham and St Helens - stopped placing youngsters with the care firms in Rochdale as a result of Mr Lambert's remarks.
In 2014 the local elections in England will see 67 shire district councils, 18 unitary district councils, 36 metropolitan district councils electing a third of councillors, plus elections for all of 32 London boroughs.