The former Olympic gymnast was injured during training for the Channel 4 winter sports show in Innsbruck, Austria, forcing her to withdraw from the programme and undergo an operation on fractured vertebrae.
In an update posted to her official website over the weekend, Beth, 30, thanked everyone for their well wishes and assured them she's continuing to recover.
"The medical staff here in Austria have been fantastic and I couldn't have wished for better people to be around me at this time. I've started to feel a lot better in the past 24 hours and I've begun walking by myself," she wrote.
"It's still a case of taking one day at a time, but I'm setting myself goals and I'm determined to be up and about as soon as I can. The doctors are happy with my progress and next week we will have a better idea of when I can be discharged from hospital. Thank you to everyone that has sent me get well messages. My Mum and Dad have been reading them to me and, one day, I'll be able to reply to you all, it really has meant a lot to me, so thank you."
Beth is Britain's most successful gymnast and has represented great Britain at three Olympic games, winning bronze at London 2012. She retired from professional competition in 2013.
She is just one of six celebrities injured during training for this year's show: fellow athletes Rebecca Adlington and Linford Christie also pulled out, while Made In Chelsea's Mark-Francis Vandelli, actress Tina Hobley and TV presenter Joe Swash have all hurt themselves.
The injuries have led some viewers to brand The Jump too dangerous for TV and suggest it should be axed. Channel 4 has said: "All winter sports carry some element of risk but in light of the number of injuries this year, Channel 4 asked producers to review safety procedures again. Whilst we are satisfied they, of course, meet safety standards, additional precautions like extra crash pads and simplification of some courses will be used."
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