The charity said almost 440,000 supplies went to children.
The Funniest Joke At Edinburgh Fringe
The pun specialist scooped the gong for Dave's Funniest Joke of the Fringe with a play on words in Punderbolt, his first hour-long show in the Scottish capital.
The 39-year-old took first place with 23% of voters with the line: "I just deleted all the German names off my phone. It's Hans free.''
Walsh, who won the first UK Pun Championship last year, saw his quip beat jokes about Kim Kardashian, hippos and Jesus to win the award, now in its eighth year.
He said: "I am delighted to win this award. What a punderful feeling. Thanks Dave.''
Walsh also created a Pun Guide to the Fringe for this year's Festival, consisting of an animated video punning the name of almost every comedian performing in Edinburgh 2015.
The competition has previously been won by luminaries including Tim Vine, Rob Auton, Stewart Francis, Zoe Lyons and Nick Helm.
A judging panel of 10 critics drew up a shortlist of gags which were then voted on by 2,000 people, who did not know which comic had said them.
This year's shortlist included the youngest entry in its history, with 12-year-old Grace the Child finishing tenth with a one-liner from her show Playground Politics.
:: Dave's Top 10 Funniest Jokes from the Fringe Festival 2015
1 "I just deleted all the German names off my phone. It's Hans free'' - Darren Walsh
2 "Kim Kardashian is saddled with a huge arse ... but enough about Kanye West'' - Stewart Francis
3 "Surely every car is a people carrier?'' - Adam Hess
4 "What's the difference between a 'hippo' and a 'Zippo'? One is really heavy, the other is a little lighter'' - Masai Graham
5 "If I could take just one thing to a desert island I probably wouldn't go'' - Dave Green
6 "Jesus fed 5,000 people with two fishes and a loaf of bread. That's not a miracle. That's tapas'' - Mark Nelson
7 "Red sky at night. Shepherd's delight. Blue sky at night. Day'' - Tom Parry
=8 "The first time I met my wife, I knew she was a keeper. She was wearing massive gloves'' - Alun Cochrane
=8 "Clowns divorce. Custardy battle'' - Simon Munnery
10 "They're always telling me to live my dreams. But I don't want to be naked in an exam I haven't revised for...'' - Grace The Child
The research also said there appeared to be a "weakening'' in support for independence.
The controversial policy was introduced in April as part of wider welfare reforms.
The Justice Committee has been carrying out an investigation into the work of the Crown Office and Procurator Fiscal Service (COPFS).
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