The former TOWIE star was being taken home after appearing on ITV's Lorraine when the incident occurred.
She tweeted: "My day started of lovely with a nice chat with @ITVLorraine this morning about my new book & all things health & fitness..
".. But I'm a little shaken up after my @AddisonLeeCabs driver crashed on my way home what a morning."
Addison Lee told the Mirror: "We are investigating an incident that took place on the A12 this morning, involving an Addison Lee driver.
"We can confirm no-one was injured and we are resolving the matter internally with all the parties involved."
A spokesperson for Lucy said: "Lucy was involved in a small car accident this morning but is fine."
Lucy finally opened up about her relationship with Louis Smith today, while speaking to Lorraine.
She said: "He's a really lovely guy. Nothing happened on between us on the show.
"But I regret that – Maybe I would have got higher scores!"
Lucy and Louis met while competing on celebrity gymnastics competition Tumble.