Not a single child refugee from Greece or Italy has arrived in the UK under a scheme to help settle lone children since the dismantling of the Calais migrant camp a year ago, with 280 empty places offered by councils going unfilled.

On the anniversary of the closure of the camp on the French coast, the chair of the home affairs select committee, Yvette Cooper, called for the overhaul of the so-called Dubs scheme, saying it was “truly shocking” that councils were still waiting for child refugees to fill the places.

The scheme was created by an amendment from the Labour peer Lord Dubs, which was passed in April 2016 and intended to bring 3,000 lone refugee children stuck in camps in Europe to Britain.

After around 200 unaccompanied children were brought over from France, the government said in January it would limit the total number arriving under the scheme to 350, but then backtracked several months later and offered an additional 130 places.

However, the home secretary, Amber Rudd, admitted during questions from Cooper at a select committee hearing last week that 280 places offered by local authorities had still not been filled but said the government was committed to doing so. “I believe it is right we help the most vulnerable children,” she said. “We have sent ministers over, we have sent officials over, we are committed to filling them.”

Not a single child or teenager has ever arrived in the UK under the Dubs scheme from either Greece or Italy, where more than 8,000 unaccompanied asylum-seeking children have registered over the past year.

The refugee charity Safe Passage is to seek a judicial review next week on behalf of a 16-year-old Syrian boy seeking a transfer to the UK, who has been assessed as severely traumatised and vulnerable.

The charity said the boy had registered his application to be considered for the Dubs scheme and transfer to the UK eight months ago but was still waiting for a date, despite receiving confirmation from a London council that they would support him. Safe Passage said the boy had been moved to protective police custody because of his severe vulnerability and the lack of places in official shelter.

Safe Passage’s Beth Gardiner-Smith said: “This highly vulnerable boy’s life has been on hold for a year and a half because of the delays to implementing the Dubs scheme.

“There is a local authority place in Britain already waiting to provide him with the care he needs to begin rebuilding his life. He should now be transferred immediately rather than left waiting whilst his condition deteriorates.”

Cooper said she wanted to see the government commit to major reform of the scheme on the anniversary of the demolition of the Calais “Jungle” camp.

Currently children and teenagers are only eligible for the Dubs scheme if they can show they arrived in Europe before 20 March 2016, but Cooper said the date needed to be brought forward because it was preventing Greece and Italy from effectively managing the relocation process effectively.

She said the design of the scheme was “too bureaucratic and complicated” for overwhelmed Greek and Italian authorities to operate. “They need to reform it urgently. The government’s failure to help these children and teenagers is shameful. It should not be beyond the wit of the Home Office to urgently sort this out.”

Cooper said the government also needed to revisit the number of places available, with some councils potentially able to offer more places than were currently listed, as well as guaranteeing the scheme would remain open, rather than close once the total of 480 spots are filled.

“Parliament passed the Dubs amendment so Britain could do its but just as we did with the Kindertransport that brought Alf Dubs to sanctuary in Britain many years ago,” she said. “Yet one year on from the clearance of the Calais camp the Home Office has failed to take any Dubs children or teenagers from Greece or Italy, even though they have thousands without proper support.”

A Home Office spokesperson said the UK was transferring child refugees to the UK using a number of schemes, including the Dublin framework where children have the right to be reunited with family members. “The UK has a proud history of hosting, supporting and protecting those in need, including some of the most vulnerable children affected by the migration crisis,” the spokesperson said.

“In the year to June 2017, the UK granted asylum or another form of leave to over 9,000 children and more than 42,000 children since 2010. At the request of the French Government, the UK put in place an expedited process, which resulted in over 750 unaccompanied children being transferred to the UK in the autumn of 2016. We continue to work to transfer eligible children here quickly and safely under the Dublin Regulation and the Dubs Amendment.”