The British prime minister insists he is intervening in the case of a British grandfather potentially facing 350 lashes in Saudi Arabia.
74-year-old Karl Andree was caught with home-made wine in the boot of his car - but his family fear the punishment could put his life at risk.
His son Hugh welcomes David Cameron stepping in, but says more must be done:
Mr Andree was sentenced to 12 months in jail by a Sharia court after police found home-made wine in the boot of his car in Jeddah last year.
Alcohol is banned under Islamic law in Saudi Arabia where Mr Andree has lived for the past 25 years.
Mr Andree has now served his sentence but has been held in jail for a further two months - and now faces a public flogging.
It has been reported that the UK has repeatedly received assurances that Mr Andree would not be flogged as a result of his crime. However it is thought it is still uncertain whether the punishment will go ahead.
Mr Andree's children Hugh, 46, Kirsten, 45, and Simon, 33, fear the grandfather-of-seven will not survive the punishment as he suffers from asthma and is frail after surviving cancer three times.
The oil executive's youngest son said he was pleased Mr Cameron was now to intervene.
Simon Andree said: "I am pleased. It has taken an awful long time."
Meanwhile, British officials stressed that the scrapping of a justice contract with Saudi Arabia was separate from the intervention in the case of Mr Andree.
Authorities in Britain had been under intense pressure not to push ahead with the proposal for £5.9m (around €7.9m) of training consultation because of a number of controversial cases in the Gulf state.
The prime minister's official spokeswoman said: "This bid to provide additional training to Saudi Arabia has been reviewed, and the Government has decided it won't be proceeding with the bid."
She added that the ministry of justice had examined its "priorities" and made a decision to "focus on some of the domestic priorities we want to do in terms of reforms here".
"Having looked at it further again, we have established that we can withdraw at this stage, there will be no financial penalty and consequently that decision has been taken," she added.
Labour leader Jeremy Corbyn accused the government of performing a U-turn.
He said: "David Cameron has been shamed into a U-turn on this terrible contract, but why on earth was it set up in the first place?
"We should be sending a strong message to repressive regimes that the UK is a beacon for human rights and that this contract bid is unacceptable in the 21st century, and would damage Britain's standing in the world."
Mr Corbyn used his Labour conference speech to call on Mr Cameron to intervene to stop a Saudi 17-year-old being beheaded for taking part in an anti-government demonstration. He said he should start by scrapping the justice ministry's bid.
