"She said 'I'm writing episode five of The Syndicate, and I'm writing this character, Alan Walters, and you keep coming into my head, will you come and do it?' and I said, 'yeah of course'.
"It's always nice to play a part that's been written with you in mind."
Even if it's the part of a twice-divorced alcoholic with a troubled relationship with his family?
"Obviously it's not a pulling part," he says with a laugh.
"Alan's got a shelfload of problems, but I think she knew it was something I could get my teeth into. I enjoy playing fraught characters, because their story is always more interesting than the perfect ones."
On the surface you might say Alan Walters actually has some similarities with King Robert Baratheon, though Addy plays them as very different men.
"They both like a drink, and both have complicated family relationships. But they've been created in very different ways. Obviously with Robert Baratheon, I read the books, and that gave me his entire history. It tells me exactly what happened to him, and why he is the way he is, so when you meet him for the first time, the whole history is there.
"But with Alan, you have to fill those gaps in yourself, and decide why his marriages failed, and how his drinking started, and when did it become an overpowering obsession.
"So while we end up with some similar character traits, they're from very different origins, and a different journey."
Alan is one of the five members of a lottery syndicate at an NHS hospital in Yorkshire.
The other four are nurses, while Alan is an orderly, and they all live a somewhat precarious existence, on the difficult treadmill of never having enough money.
That is until they win £72 million. The newfound riches are obviously a great boost in many ways, giving them wider dreams, but the money doesn't change everything for the better.
"It makes no difference to those innate personality qualities, and Alan just has this knack for very poor decision-making.
"So it was interesting to think about what would it feel like for him to have that much money, and why he would keep making stupid mistake after stupid mistake after stupid mistake."
It's not all doom and gloom for Alan, though - he does want to make things right with his family, even if it might be too little too late.
"It's not a smooth ride, but there is a ray of hope at the end for him."
TV profile
Who: Mark Addy
What: Season two of The Syndicate
When and where: Tonight, 8.30pm, UKTV