British Rowing confirmed she was in a "stable but serious condition" after falling down the stairs earlier this month.
Peter McCabe, Chief Executive of Headway, said: “On behalf of everyone associated with Headway – the brain injury association, I would like to express the charity’s support for not only Anna but also her family, friends and colleagues.
"As a charity that helps people affected by brain injury, including families whose loved ones are in the acute phase of treatment, we would like to offer our help to Anna’s family and friends at this difficult time."
Headway supported James Cracknell and his family when he sustained a brain injury while cycling in Arizona, a petrol tanker travelling at around 65mph struck him as it passed in 2010.
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