"There was lots of giggling, eye contact and touching as they sat together near a couple of trees.
"They looked like they had known each other for years - and the relationship was obviously more than just friendly."
One of Brand's pals told The Sun last week: "Things are getting very serious between them - they're a proper couple now. They had met several times in the past, but really got to know each other during the Olympics.
"People thought Russell was joking at the time, when he said he had a crush on Geri all over again, but it was true," the insider said.
"They just clicked - they have so much in common."
And while the dating rumours swirled, the pair was papped by TMZ shutterbugs as they left the singer's London home last Wednesday.
'Just friends'
But other sources have poured scorn on the romance reports, claiming that the pop singer and the funnyman are just friends.
"Russell and Geri are just friends and have been out a few times of late," an insider told Us Weekly. "A few media are prematurely reporting that they are in a serious relationship, [but it's] a little early for all that type of speculation."
Chimed another: "They're just friends and have been out a few times, there's not much else to add at this stage."
But according to Metro, Halliwell has confirmed she is romancing the comic.
"Yes. It's been a whirlwind," the 40-year-old is quoted as telling the website.
"Is he my ideal man? I'm choosy. I want someone who's trustworthy, sweet and kind."
She added: "All I want is to be in a loving relationship."
Halliwell's comments follow reports that the fledgling romance is already on the skids.
The Sunday Mirror claimed that Halliwell is finding the comedian a bit "too intense".
"Things are already cooling off," a source told the paper. "Russell's way into very intense spiritual readings that are just too much, even for Geri."
Brand, 37, apparently put off Ginger Spice when he turned up at her home in Highgate, North London last week with a DVD of Alan Bennett's Talking Heads to watch together.
"He is way too intense, full stop," the source continued. "He turned up with Talking Heads ... it went straight over Geri's head.
"I don't think she really fancies him. She's just enjoying the attention. It will be yoga, sex and fizz, but it won't last the distance. He's off back to LA soon and she's not planning on going with him."
'Cheeky little minx'
Band mate Melanie Chisholm recently revealed that Halliwell has kept the status of her relationship with Brand a secret from her fellow Spice Girls.
Quizzed about the romance, she told Magic FM: "I don't know what's going on. I know they get on really well. I am sure they are just friends. I'll have to quiz her on that one, the cheeky little minx!"
Halliwell played coy about a new relationship in a recent interview with Hello! magazine.
"I'm not going into details," the singer said. "Right now there's nothing serious. I was a late starter on the romantic front. I didn't start dating until I was in my 30s ... I quite like having somebody to cuddle. I like that intimacy, it would be wonderful."
Brand recently ended his relationship with Isabella Brewster. His divorce with pop star Katy Perry was finalised in August.
Fast gossip
And finally...
* Michael Phelps throws retirement party in Sin City.
* Lady Gaga flashes new ribcage tattoo.
* Hollywood reacts to Green Mile actor Michael Clarke Duncan's death.
* No, Bruce Willis isn't suing Apple over iTunes.
* Bobby Brown declares himself 21 days sober after rehab stint.
* Beyonce snubs Kim Kardashian at Jay-Z festival show.
* Are Chris Evans and Minka Kelly a couple once again?
* Elton and Madonna kiss and make up?
* Kristen Stewart covers British Vogue, still struggles with fame.
* Listen: Alicia Keys and Nicki Minaj team up for new track Girl On Fire.
* Noel Gallagher's stowaway spider causes backstage quarantine.
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