Accusations of democratic disaster as David Jamieson elected as PCC on even lower turnout than for predecessor Bob Jones

Only one in 10 registered voters took part in a byelection for a police and crime commissioner (PCC) in the West Midlands, prompting Labour accusations of "a shambles".

The vote following the death last month of Bob Jones resulted in a turnout of 10.4%, the lowest recorded since the posts were created two years ago, prompting demands for the process to be reformed.

The four-way contest on Thursday, for which the count was done on Friday, was won by David Jamieson, a former Labour transport minister and former MP for Plymouth Devonport, who won more than 50% of the vote. Only 201,789 legitimate votes were cast and another 3,667 rejected. The turnout was lower than the 11.96% recorded for Jones, a long-serving local politician, during the first elections in 2012. The lowest turnout that year was in Staffordshire with 11.6%, and the national turnout was 15%.

The cost of the election to the taxpayer has been estimated £3.7m, just under £20 for each vote cast. Shadow home secretary Yvette Cooper tweeted: "Crazy that Theresa May's PCC legislation has meant election in August costing £3.7m where 9 out of 10 people didn't vote". Jack Dromey, her party's spokesman on policing, said the byelection was "characterised by costly chaos and a record low turn out".

The legislation that brought the PCC system to England and Wales was passed in 2011 with the first elections the following year. A byelection must be held within 35 days once at least two people indicate to the election authorities that there should be a poll. This meant voting had to be held in the middle of the summer holidays and in the a week before the August bank holiday.

Dromey called the law "a shambles", benefiting neither candidates nor electors. Labour was consulting on the future of the posts, having opposed their introduction in the first place, but would not be making "a snap decision" as to whether they would be scrapped.

The Electoral Reform Society said the law needed looking at after the "very depressing turnout". Research officer Chris Terry said: "I think it could have been better had more thought been put into the process of how the byelection was run."

Alexandra Runswick, director of Unlock Democracy, said the turnout had been a disaster, putting the future of the commissioner role in doubt. "This level of turnout stretches the legitimacy of the office to its limit."

Policing minister Mike Penning insisted PCCs were making "a real difference" but added: "I am of course disappointed with yesterday's turnout, but we must bear in mind this was a byelection taking place in August following the sad death of Bob Jones."

He added:"Around 200,000 people voted yesterday, whereas nobody voted for their old police authority. Our police reforms are working and crime is down more than 10% under this government."

Ukip trounced the Liberal Democrats, but Nigel Farage, the only one of the four candidates' party leaders to make a campaign trip to the region, said there was "no public appetite" for the byelection as well as "a wholesale failure to explain to people the changes that are happening".

Jamieson, 67, a former Labour transport minister, who promised an extra 450 "bobbies on the beat" if elected, said he was delighted with a win, but branded the legislation "messed up" and accused the government of not doing enough to promote the role.

Asked about the size of the vote in a separate interview, he told the BBC: "People in an election in a democracy can choose to vote or not to vote. There is a job to do and it's a very important job. There's a huge budget of £540m [which] has to be spent on our policing."

Nick Alston, chairman of the Association of Police and Crime Commissioners, said the elected role was "invaluable" in holding the police to public account. "The turnout was lower than we would have preferred but that does not detract from the important work that police and crime commissioners across the country carry out every day."

The West Midlands poll was hosted by Birmingham city council, although paid for by the Home Office.

Full result: David Jamieson (Lab) 102,561 (50.83%, +8.82%), Les Jones (C) 54,091 (26.81%, +8.29%), Keith Rowe (Ukip) 32,187 (15.95%, +8.58%) Ayoub Khan (LD) 12,950 (6.42%, -0.05%)