An independent bookseller has been deluged with thousands of requests after offering to send anyone who feels they need one a copy of Matt Haig’s memoir about depression, Reasons to Stay Alive, in an initiative the author called “such a positive thing on what was a pretty bleak weekend”.

Simon Key, who runs online retailer the Big Green Bookshop, was contacted by a reader, Emma, offering to buy a couple of copies of Haig’s book for people in the wake of TV presenter Caroline Flack’s death. Haig’s book details his own descent into depression, and his climb back out of it.

Key, who already runs a weekly “buy a stranger a book” club, told his Twitter followers about her offer, and said he’d “try to cover any others that are requested”. As thousands of requests poured in, readers were also quick to support him with donations.

“People have been very generous – some have given a pound or two; others more than £100,” Key said. Donations now stand at around £6,000 and are still coming in, with Key having sent out more than 600 books. He is still making his way through the requests he’s received – “I’m posting about one a minute,” he wrote on Twitter on Sunday - shortly before he leaves for a half-term holiday.

“I’m getting thousands of DMs from people who need the book, and who are telling me why,” Key said on Monday. “This book has made a difference – lots of people have said it saved their lives. And this is not just about people getting the book, it’s about how they’re getting it. They’ve been brave enough to ask for it, and that’s a step forward.”

Blackwell’s in Oxford has also been giving away copies of the book to those who have asked for it, also funded by readers. Deputy manager Charlie Bush said the shop now had 40 books donated by readers, with the retailer discounting the price for donors and covering the postage costs.

“We really believe that books have the power to be life-changing and we also know that lots of people are going through tough times for all sorts of reasons. So we hope that people can gain some comfort and inspiration from Matt’s book. We tip our hats to Big Green Books for getting the ball rolling and offer huge thanks to customers who are making this possible with donations,” said Bush.

Flack had described Haig’s book as “honest and beautiful” on Twitter in 2015 and in the aftermath of her death, the author said that “when I had a bout of Twitter-fuelled depression just as Reasons to Stay Alive came out, this was the tweet that first lifted my spirits. We need more kindness.”

On Monday, Haig told the Guardian that the giveaways were “amazing … such a positive thing on what was a pretty bleak weekend. The response was phenomenal, and the generosity of so many people who volunteered to give copies to other people – online strangers – was, well, there are no words. It was just very touching and shows that the internet, and life in general, are a lot better when we try to look after each other. I am also pleased that this book, which I wrote over five years ago, is still able to help people in some small way.”

• In the UK and Ireland, Samaritans can be contacted on 116 123 or email jo@samaritans.org or jo@samaritans.ie. In the US, the National Suicide Prevention Lifeline is 1-800-273-8255. In Australia, the crisis support service Lifeline is 13 11 14. Other international helplines can be found at www.befrienders.org.