The upshot has been 'ten front pages in the past two weeks', and Slattery is delighted. 'Publicity is our oxygen. It's my job to keep it flowing,' he says.
When Turner decided to end her life in a Swiss euthanasia clinic, both parties recognised the opportunity for public debate. 'I asked the Turners whether they would be prepared to put the process in the public eye, and after some deliberation they agreed,' Slattery says. 'Obviously I had to use journalists I could trust.'
In the end, just two – BBC health correspondent Fergus Walsh and Press Association legal affairs correspondent David Barrett – accompanied the family. Both did 'a first-class job', says Slattery.
Back at Dignity in Dying's HQ in London's Kensington, the thoughtful and quietly spoken 37-year-old confesses to being slightly nervous about our interview. 'I'm normally briefing other people for interviews,' he says, taking a final scan of a media 'cheat sheet'.
After finishing law school Slattery, brought up near Birmingham, baulked at going into the legal profession, preferring to 'deal with real people'. Following a spell at Birmingham's water industry watchdog, he became parliamentary media officer at Ofwat. Four years later he joined the National Lottery Commission as head of public affairs – shortly before Sir Richard Branson took it to the High Court.
'I like proper issue stories, not fluff, and I get bored when things slow down,' he says. 'I've been described as a natural campaigner, and I love the cut and thrust of dealing with the media.'
Independent on Sunday senior journalist Severin Carrell describes Slattery as 'straightforward and easy to deal with. Too many people in PR try and bullshit you, but Mark doesn't. There's nothing devious about him'.
However, his philosophy of tackling things head on put him at odds with his former boss Mark Harris, still CEO at the Commission.
'Harris's policy of "managed silence" did not sit well with me,' Slattery explains. 'He once said "you are a front-foot player; I am a back-foot player".' Harris was unavailable to comment on the two men's working relationship, but Slattery's replacement Sarah Hanratty was 'amused' by his comments, insisting that Harris has an 'open-door policy' with journalists.
Although outwardly serious, Slattery has a wry sense of humour, evident when he tells the story of the Commission's initial rejection of Branson and Camelot's bids in 2000. 'We thought no one had rumbled us,' he says, 'but two days before it was due to be announced, Rupert Steiner from The Sunday Times rang me and said: "Don't tell me, neither has won?" It took a split second to realise he was joking. I held my nerve and laughed it off.'
Slattery's time at the Commission also generated a headline that still triggers a smile, when the Daily Mail asked its readers: 'Would you trust this lot to run a whelk stall?'
'If things get bad, I dig it out to remind me it's never that bad,' he grins, remembering his 'delight' at the more recent coverage of Dignity in Dying's new name. 'We couldn't believe it. It would have cost us thousands in ads or PR. It even crossed my mind to send [the critics] some flowers, though someone suggested a wreath would be more apt.'
Unmarried, but with a long-term partner, Slattery is a keen writer, contributing to the New Statesman, Cricketer magazine and a forthcoming book on the lottery. A year and a half after taking a significant pay cut to join a small charity, does he think he made the right choice? 'Yes,' he asserts. 'This has been the busiest and most interesting 18 months. And anyway, I've never been particularly interested in money – or, indeed, any good with it.'