The Sun reports that the couple have been on a number of dates including a tour of Hampton Court Palace last weekend.
A close friend of Russell has told The Sun that things have gotten serious between the two over the past couple of weeks.
They told The Sun: "Things are getting very serious between them- they're a proper couple now"
"They just clicked- they have so much in common...he is spending so much more time in London just to be with her."
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Russell and Geri apparently got to know each other during rehearsals for the Olympics closing ceremony where they both performed.
After the ceremony, Russell reportedly told The Daily Star: "It's like going back to 1996. I've got a massive crush on Geri Halliwell, so everything in the world was as it should be."
But now it seems that things have developed into more than just a crush.
Another close friend of Russell's told The Sun: "He has ended his relationship with Isabella Brewster, and is now dating Geri properly."
"They've exactly the same sense of humour and are serious about clean living."
An onlooker at Hampton Court Palace told The Sun that the Geri and Russell didn't seem to care who knew about their relationship either.
He said:"They seemed like they were having a really great time, holding hands and chatting- it was 100% obvious they were a couple."
"Geri was holding his hand the same way I hold my wife's. It was so cute."