Boris and Johnson deny claims that the former nanny was fired after having a glass of wine with the former prime minister.
After three days in the job, Theresa Dawes, 58, claims she was sacked and is now considering legal action against the couple.
In accusations described by the Johnsons' spokeswoman as being 'totally untrue', Ms Dawes claimed she had been given 15 minutes to pack her bag the day after she returned to her home after giving birth this summer.
She said the dismissal came after she was invited by Mr Johnson to celebrate the arrival of the couple's third child, Frank Alfred Odysseus, with a glass of roses.
In July, she was still recovering at the hospital after giving birth on July 5 - just after giving birth. The former nanny believes that the glass of wine on the terrace was witnessed by her mother and led to her sudden dismissal.
In an interview with the Mirror, she said Johnson was 'extremely rude' after returning home from hospital, while her husband had been 'flustered'.
The following day, she allegedly received a phone call from Carrie Johnson asking to meet her at 11am, where she was told that she didn't think it was working and that we didn't gel.
She said Johnson raised comments Ms Dawes had made during a previous conversation when she said her former employer had celebrated Johnson's resignation over the Partygate scandal.
She told the Mirror that the alleged series of events was a 'complete nightmare' and that she wished she had never involved herself with the couple.
She is now considering legal action after she claims she is owed thousands of pounds for the agreed three-month contract, along with severance pay.