Conservative candidates Jason Hughes and Ronak Pandya are fighting the by-elections in Grove and Tolworth & Hook Rise wards caused by the resignation of Lib Dem councillors.
The polls were triggered when Lib Dem deputy leader Stephen Brister and long-serving colleague Vicki Harris stepped down last month. Brister had attended just one Council meeting over the past six months.
At the local elections last year the vote in Groves was finely balanced between Conservative and Lib Dem, with one councillor from each side now representing the ward. Conservative support has grown in Tolworth as a result of new Council initiatives.