Cooper and Shelby's mum, Lauren, told the BBC: "It's a very tough competition.
"Everyone who takes part is very, very good, so I'm very proud of them both.
"We are so happy that Cooper won again, but Shelby is going to be after that title next year, I think."
Shelby said she was really pleased at her place in the competition after practising and copying Cooper's technique.
Lauren said Cooper's seagull screeching success had not gone to his head – even if he would not share his top secret techniques.
"He takes it all in his stride. He's so chilled about winning again," she said.
"It has been a huge boost to his confidence.
"He's very bright, but he is a bit shy – unlike Shelby, who wants to do everything.
"His confidence has soared. He is doing so many things he wouldn't have done before, including getting a part as an ugly sister in his school play Cinderella."
How the competition works
A panel of judges awards each screech a score out of 100, and the winner is the person who gets most points.
Each judge awards up to 20 possible points, with up to five points awarded for how the competitors were dressed and the behaviour they exhibited.
The remaining 15 points are awarded for how they mimicked the call of a seagull – with attention paid to the timbre, rhythm, and variation of the efforts.
Cooper's winning score was 87, and Shelby's effort got 81 points.
There was more British success with Toby, 10, from Leeds, taking third place.
Cooper was awarded his second first-place medal and a hamper full of crisps, chocolate and fizzy drinks as a reward for his super screeching.
Lauren added: "We're definitely planning to come back next year.
"Both Cooper and Shelby are already excited about it.
"It's a really amazing event – but not one I'd ever have thought we'd have a talent for in the family."
