Three former footballers who appeared on the Victoria Derbyshire programme to tell their story of being abused as children have urged the BBC to save the programme, as journalists at the corporation prepare for a wave of job cuts to be announced on Wednesday.

Andy Woodward, Steve Walters, and Chris Unsworth have written to the BBC director general, Tony Hall, to urge him to reconsider scrapping the show, saying their emotional appearance to discuss abuse at the hands of paedophile football coach Barry Bennell helped change the law.

“We – like thousands of others – chose to speak to Victoria because we trusted her and her programme to help tell our story and aid our campaign for justice,” they said. “Over 800 victims came forward because of our interview that day. Police investigations were launched, and the government made relationships between coaches and 16- and 17-year-olds in their care illegal. A year after we went on Victoria’s programme, our abuser was jailed for 31 years for 50 counts of child abuse.”

They added: “The programme is not aimed at BBC executives, or members of parliament. It’s made for those underserved audiences that are ignored elsewhere by the BBC’s news output – and, judging by the backlash since this decision became public, it’s highly valued by those audiences. It takes risks and explores subjects that no other show dares; and it gives time and space for those interviews, not just a quick news package or a three-minute interview.”

Last week BBC bosses confirmed that the show was to be cancelled after news leaked early, leaving staff at the programme wondering if they will still have jobs elsewhere in the corporation. The decision was originally due to be announced as part of a wider range of job cuts designed to save tens millions of pounds, which will be unveiled in full on Wednesday afternoon and are expected to affect high-profile shows such as Today and Newsnight.

Other BBC staff said they had been told to expect a headline number of job cuts to be announced on Wednesday, although individuals will not immediately be told if their position is at risk. The move towards a centralised commissioning system, with pools of journalists producing stories for multiple programmes, is designed to make around £40m of budget savings. The BBC is having to pick up the cost of paying for some free TV licences for over-75s and faces a major battle with the government over its financial future.

The mid-morning Victoria Derbyshire programme is broadcast on BBC Two. Originally launched in 2015, it was seen as a cost-effective way of filling both schedules while also producing online content, with its journalism often reaching substantially larger audiences on the web than the roughly 200,000 viewers it attracts on traditional live television.

The BBC has argued that this shows the cost of producing the programme would be better directed to producing online-only journalism while losing the costs associated with making a live in-studio show.

The head of news, Fran Unsworth, has said the programme produced excellent journalism and “we will be retaining some of the programme’s journalism roles to enable us to continue this work”. Staff fear that without a ringfenced team they will not be given the freedom to pursue original reporting.

Derbyshire told the Guardian that her team had been overwhelmed by the public support since the news broke of its proposed cancellation. “However, we’re not surprised so many people from different backgrounds want the programme to stay – it speaks to them in a way no other programme does. It delivers original journalism that affects people’s lives and it holds powerful people to account. We are still hopeful the BBC will reconsider,” she said.

• This story was amended on 28 January to remove a reference to the reported cost of the Victoria Derbyshire programme.