Voters were not given enough information about the police and crime commissioner elections, Labour has claimed as turnout was expected to be as low as 10% in some areas.
In Wiltshire, the first force area to declare, the overall turnout was 15.8% as Tory candidate Angus Macpherson, a magistrate, won after a second round of voting ahead of Labour's Clare Moody.
But in parts of the county, the turnout was much lower. In Trowbridge, it was as low as 10.95% according to unofficial counting, while in Devizes it was 10.41%. In Humberside, where Lord Prescott's name on the ballot paper raised the profile of the election, it was 19.48%, East Riding of Yorkshire Council confirmed.
Shadow home secretary Yvette Cooper said the elections for the new commissioners had descended in to a shambles, with many voters taking to Twitter to describe the low turnout at their polling stations.
Labour criticised the Government for not doing enough promote the elections. Ms Cooper said: "We warned the Government repeatedly that they had the wrong approach and that turnout would be low. Theresa May and David Cameron didn't listen and it is shocking that they have spent £100 million on these elections rather than on 3,000 police constables instead."
In the most radical shake-up of the service for half a century, the new commissioners, who are expected to earn up to £100,000 a year, will control police budgets, set priorities and have the power to hire and fire Chief Constables.
Elections are being held in 41 police areas outside London. The Electoral Reform Society predicted a turnout of 18.5%, which would be below the previous record low in a national poll in peacetime of 23% in the 1999 European elections.
Asked if the expected low turnout would be a disaster, police and criminal justice minister Damian Green told ITV's Daybreak: "It's a new idea and as will all new ideas it will take some time to get going. The measure of this policy is not the turnout, it's what the police and crime commissioners achieve over the next few years."
Labour MP Chuka Umunna described the PCC elections as absurd. He told the programme: "The Independent Electoral Commission said that the way they (the elections) have been run has been a comedy of errors.
"It has been a total shambles and the £100 million spent on it could have been spent on 3,000 police officers. At least if you are going to have the elections, organise them properly and don't have them in the middle of winter."