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The couple, who welcomed son named Bingham in July 2011, announced their engagement in April.
And now Hudson's mother, Oscar winner Goldie Hawn, 66, may have let marriage news slip during an interview with the U.K.'s Evening Standard's ES magazine, reports the Vancouver Sun.
"When my daughter Kate married an English rock star it didn't worry me," Hawn is quoted as saying. "All that matters is that the relationship is a good one."
Last weekend, the 33-year-old Hudson and Bellamy certainly looked like a happy couple: They were spotted lolling on the beach and cuddling in the surf in Cancun.
Just before their engagement, Hudson told InStyle what she loves about her British beau. "I love that Matthew knows how to express himself," she said. "He shows his love. He communicates."
This would be the second marriage for Hudson, who was previously married to Black Crowes singer Chris Robinson. She and Robinson also have an 8-year-old son, Ryder.