Friends of the Welsh singer, 33, said she was "sad but moving on" after six months of dating Adam, who is one of Prince Harry's closest friends.
The pair's relationship is said to have become strained after Adam began spending more time in the gym training for an upcoming charity boxing match.
"Adam has been training really hard for this boxing match and has been really under the cosh [under pressure] at work," a source told the Daily Mirror.
"It was Katherine's decision but she still loves Adam and will continue to support him as a friend. Despite this she is incredibly sad and feeling pretty raw – splitting up is always painful."
Adam, who is a former professional rugby player, is due to fight Richard Branson's son-in-law, shipbroker Fred Andrews, at black-tie fundraiser Boodles Boxing Ball on 21 September.
Katherine and Adam were introduced through mutual friends and officially started dating in February. vThe romance was Katherine's first since she called off her engagement to welsh TV presenter Gethin Jones in December 2011.
At the time of the break-up, she told friends that she was "devastated" and "beyond broken-hearted".
She was also in a six-year relationship with Steve Hart, a member of the 90s boy band Worlds Apart.
Katherine once opened up about having relationships in the public eye. "Public break-ups are difficult," she said.
"Going through that is devastating anyway but when it's 'out there' people feel free to comment.
"My big dream is children and getting married. For women in my business it's very difficult to decide when to stop. But I can't wait to be a mum and if – please God – I am, I think it's a gift and I want to enjoy it."