A woman told she had to wait 17 weeks for screening after finding a lump in her breast has discovered she has cancer following a private test.
The trust says it is getting 80 mammogram referrals per week
The 37-year-old mother-of-three from Cardiff has had surgery to remove a tumour and part of her lymph gland.
She is waiting for the results of tests to see if the cancer has spread.
Cardiff and Vale NHS Trust apologised, and said that despite introducing extra clinics, patients were still waiting too long.
The case is similar to that of Theresa Debono from Cardiff, who was also told she would have to wait 17 weeks before having a mammogram.
Mrs Debono paid privately for a mammogram, but following further tests discovered she did not have cancer.
Theresa Debono was given the all-clear after tests
In this latest case, the woman, who wants to remain anonymous, said reading about Mrs Debono's case had prompted her to call the University Hospital of Wales to find out how long she would have to wait for her mammogram.
When she was told more than four months, she contacted private health company Bupa. She had to pay £144 for the test and £100 to see the consultant.
Her test proved positive, and she had surgery three weeks later at Llandough Hospital near Cardiff.
Surgeons also removed part of her lymph gland to examine as they feared the cancer might have spread.
She will receive the results of the tests on Thursday, which will determine whether she just needs radiotherapy or chemotherapy as well.
She told the BBC Wales News website: "It was only because I read an article about Mrs Debono that prompted me to ring up, otherwise I would have waited.
"They told me over the phone that they were telling everybody it was 17 weeks. They told me then that my case had been classed as urgent.
"I was annoyed about it. It is a long time. They knew from my GP that my mother had had breast cancer.
"I have nothing but praise for the hospital staff. It's just the waiting list - once you are in there, they do look after you.
"They all seem to be aware that there's a problem and they are annoyed with it themselves."
Two years ago, the woman had to wait a only few days to have a mammogram carried out within the health service.
Susan Morgan, a relative of the patient, criticised the Welsh assembly government's spending priorities on health.
"I hate to think how much more advanced it would have been in five months' time if they had not been able to go private.
"I think it's a disgrace. The priority seems to be to give old people free swimming lessons instead of the real priorities which is saving lives," she said.
"They say breast cancer is inherited. You would have thought that they would have made some special efforts to get her in earlier.
"I can't understand why she had to wait so long."
A statement released by the Cardiff and Vale NHS Trust said they could "only apologise" for the distress caused to the patient.
A spokeswoman said additional short-term clinics been had running at the University Hospital of Wales and neighbouring trusts for several weeks.
"With these measures in place the maximum waiting time for patients is now approaching eight weeks, down from 17 weeks." the statement continued.
"This is still too long and will be reduced further in the coming weeks as the new clinic arrangements have a greater impact on waiting times.
"We expect to reach the 10-day target, for patients referred to the breast service to have an outpatient appointment, by February 2005.
"For some time now the trust's breast service has received around 80 new referrals each week while only having the staff and facilities to deal with a maximum of 60 new referrals each week.
She added they were in discussions about a sustainable long-term solution but said one could only be achieved with additional investment.
A spokesman for the Welsh assembly government said the health minister, Jane Hutt, was concerned to hear of another "unacceptable delay" for a mammogram and had asked for further details of the case.
"When problems of waiting times for mammography treatment were first brought to her attention, the health minister expressed strong concern to Cardiff and Vale NHS Trust," he said.
"The trust has been briefing the minister regularly on improvements that are being made and the minister is encouraged by the fact that the trust is now reporting a waiting time of eight weeks, when previously it had been 17 weeks.
"The trust has also reassured the minister that the required 10-day target will be met by February."
A motion of no confidence in the assembly government's health policy tabled by Plaid Cymru was defeated in a vote in the chamber on Tuesday.
The assembly government won by 29 votes to 25, with the motion winning support from other opposition AMs.