The 52-year-old former Countdown star ended up in hospital following the fall and has been forced to cancel TV appearances following the accident.
Vorderman admitted she felt “like a complete idiot” after she ran down the stairs with her hands in her pockets following a meeting in central London.
The Loose Women presenter’s boyfriend, ex-Red Arrows squadron leader Graham Duff, took her to hospital where she had surgery on her face.
Vorderman, who has a plaster cast on her nose, said: “I feel OK but, because I had my hands in my coat pockets while I was running, I had nothing to break my fall except my head.
“I really do look like I’ve done eight rounds with Muhammad Ali.
“The bruising round my eye has reached its peak. I have stitches in my forehead and left eyelid.”
Vorderman, who also presents Food Glorious Food, added: “I am just counting my blessings that I didn’t damage my skull or the left eye itself...”
A friend said: “The fall was really nasty.
“Thankfully, she hasn’t done lasting damage, although the bruising will look horrific over the next few days.
“Luckily, Graham is there to help nurse her through it all.”