Britain's most successful female Paralympian issued the warning on social media after a visit to Lyme Park in Disley, Cheshire.
She said she was 'centimetres from being the victim of a dog attack' at the parkland.
Lyme Park has also responded to Dame Sarah's experience and has reminded ALL dog walkers of their responsibilities when using National Trust parklands.
Dame Sarah, who is now the Active Travel Commissioner for Greater Manchester, wrote of her experience on X.
She wrote: "Centimetres from being the victim of a dog attack whilst in @NTLymePark this afternoon.
“Absolutely scared the life out of me & not 100% sure what I did that resulted in making the dog leave me alone but I’m so glad it did. Please put your dogs on a lead.”
She later went on to thank friends and followers for their messages after the near miss. She said: “Thanks for the messages of concern, I’m ok, but as someone already scared of dogs after being bitten as a child, it’s not done much to help that improve.”
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