Marie Rollason might have survived if the clot had been detected earlier, the hearing was told.
Mrs Rollason visited the hospital's A&E department twice in the weeks before her death on December 29 last year.
The 43-year-old had been suffering from collapses, but these were attributed to a head injury sustained after she tripped and fell in the bathroom of her Wolverhampton home earlier that month.
Giving evidence at the inquest, consultant Rakesh Khanna said abnormalities in the results of an ECG test were a 'potential red-flag' – but the junior doctor who assessed Mrs Rollason decided she could be discharged without further investigations following discussions with a locum consultant.
Dr Khanna added had the clot been treated following the test performed six days before Mrs Rollason's death, she 'more likely than not' would have survived.
But he also explained she had not displayed the predominant symptoms classically linked to a pulmonary embolism.
Coroner Zafar Siddique concluded: "On the balance of probabilities, had further tests been ordered and Mrs Rollason had been kept under observation, a basic medical procedure would have detected the pulmonary embolism and more likely than not she would have survived.
"The lack of such tests and decision to admit does amount to a gross failure in basic medical care. Had those measures been taken, it is likely Marie would have survived.
"My conclusion is she died of the medical cause, contributed to by neglect."
Mrs Rollason's husband, Lee, told the inquest she was a 'bubbly' woman who had worked as a catering assistant and had few health concerns.
She first visited A&E on December 19 after the fall at the family home in Springhill Avenue, Penn, shared with children Lewis, 16, and Owen, 11. Doctor Khanna said her treatment at this time followed 'standard lines'.
Over the next four days she suffered up to five episodes where she fainted or lost consciousness altogether – but Mr Rollason attributed them to anxiety.
After collapsing at her GP surgery she was taken to A&E for a second time on December 23. She was again sent home and advised to ask her doctor to refer her to a cardiologist if she passed out again.
At this point Mr Rollason said he was told the results of the ECG were 'normal' despite the abnormalities.
Over Christmas she was fainting less often and the family had hoped she was on the mend.
But following a fall at her GP surgery on December 29, she again passed out and this time failed to regain consciousness and died.
Doctor Khanna, who has worked at New Cross for 15 years, said the ECG results had shown 'non-specific' minor changes which he would consider consistent with relatively poor blood supply running through the heart.
He said: "I would have been a little bit concerned and possibly would have considered admission. It is difficult to say because we now know what the problem was but I would have been a little bit concerned because she was only 43."
He added doctors who saw Mrs Rollason were 'anchored' on the head injury she had sustained.
Fiona Brownsword, representing the trust, said any failure in respect of the ECG test could not be described as a gross failure in basic medical care given Mrs Rollason's lack of symptoms associated with a pulmonary embolism.
But following the coroner's conclusion, Mr Rollason said he was considering legal action against the Royal Wolverhampton NHS Trust.
He said: "I think the pulmonary embolism should have been detected one way or another. We did not know what was wrong, we had no idea.
"We were exceptionally happily married as anybody who knew us could vouch for and she has left a massive void in our lives. She had a heart of gold and was my soulmate."
Dr Jonathan Odum, Medical Director at the Royal Wolverhampton NHS Trust, said: "We always strive to provide high quality, safe care for every one of our patients and we send our condolences to the family and friends of Marie Rollason.
"The Royal Wolverhampton NHS Trust will now seriously consider the verdict, the coroner's comments and the letter he is sending to the trust."