Suzanne Doherty, 42, had an operation for a gynaecological condition but was unaware she was 14 weeks pregnant.
Medical staff also failed to spot the unborn foetus and she was sent for a hysterectomy to remove her uterus.
The procedure meant the unborn baby died and when she came round doctors were forced to explain that a foetus had been found and terminated.
Ms Doherty, who was told she had lost a son she did not know she was carrying, has now been awarded a £62,000 payout after the Royal Cornwall Hospital in Truro admitted liability and a ''catalogue of errors''.
The hospital is where the Prime Minister's daughter Florence was delivered in 2010.
The latest case comes as more than 1,500 patients of the hospital's gynaecology consultant, Rob Jones, are having their cases reviewed.
The consultant, who delivered David Cameron's daughter, has since resigned and removed his name from the medical register. A review ordered by the hospital's trust is due to report back by the end of the year.
It is not known if Mr Jones was involved with Ms Doherty's care.
Ms Doherty, of St Mabyn, Cornwall, said yesterday the ordeal left her suffering depression which caused her to lose her job following the blunder in 2007.
She said: ''I was told the operation had been success but unfortunately a foetus had been discovered and that the foetus had been terminated.
"I was told with just the curtains pulled, so there were other people in the bay that heard what had happened.
"It shouldn't happen in this day and age. There are so many checks. It shouldn't get to the point where a pregnancy was missed.''
She said following the operation she was physically well but had suffered mentally leading to "long bouts of quite bad depression".
She said: "I would go back to work and then I wouldn't be able to handle it and I would be off again, which ended with me having to lose my job.
"Knowing the fact that we've got three girls and we could have had a son, that was absolutely devastating.
"It has taken me a long time to get to the point where I have accepted what has happened, but it has taken five years.
"The money we can use for the children. But that's never going to bring my son back.''
Ms Doherty said she had woken in hospital to be told the operation was a success but that "a foetus was discovered and that the foetus was terminated".
It later emerged that a consultant noted her uterus was abnormally large prior to it being removed.
Her solicitor Charlotte Skouby said the trust had admitted the pregnancy "could and should have been diagnosed at the point when it was still viable".
She said: "This would have enabled our client to go on to term and deliver a much wanted baby boy.''
Alison Millar, a partner at the firm, added: "This was a very unusual and obviously devastating case which has caused great distress to our client.
"We are very glad to have secured a settlement for them which recognises their injuries and enables them now to close this most unhappy chapter of their lives".
Mrs Doherty was given her pay-out after the Royal Cornwall Hospitals Trust said it would "not tolerate poor clinical practice".
Lezli Boswell, the trust's chief executive, wrote a personal letter of apology.
She said: "I am deeply sorry to hear about any anxiety, pain or distress caused to our patients.''
Mrs Doherty added: "The apology from the chief executive has made us feel they've acknowledged they've made serious errors.''
