Nikki Hall spoke out after Leeds Teaching Hospitals NHS Trust revealed the scale of postponed appointments between March 2020 and January 2021.
The trust said that its breast screening service is now fully operational and that extra sessions are being held at weekends to fit as many women in as quickly as possible.
Mum of one Nikki, 48, of Rodley, said her breast cancer was detected during a regular mammogram in February 2018.
The cancer was spotted before a lump had developed and Nikki had a mastectomy a month later.
Nikki was considered high risk because her mum, Ann Stewart, died from breast cancer aged 38 in 1985 when Nikki was aged 12.
"By the time she found the lump and they checked it out it was too late because the cancer had spread to other parts of her body," said Nikki.
"She died within a few months of being diagnosed - it was too late to do anything.
"I'm an only child and was extremely close to my mum. I just felt devastated.
"From the age of 18 years old I was screened once a year with a mammogram at St James's Hospital.
"It was totally unexpected in 2018 when they spotted something, which turned out to be cancer.
"I didn't feel a lump, it was caught very early. My surgeon told me the cancer was growing very fast and spreading.
"Having that scan appointment on time saved my life, without a shadow of a doubt."
Commenting on the 12,000 women who had appointments postponed, Nikki said: "It is absolutely heartbreaking and frightening because cancer may have been missed in some cases.
"I am a prime example of someone who has made a full recovery after breast cancer because I attended that screening appointment on time.
"My advice to any woman who has missed a screening appointment is to contact your doctor to rearrange it as a matter of urgency."
Nikki, who climbed Mount Kilimanjaro in September 2019 to raise awareness of the importance of screening, added: "I am only alive because I went to that screening appointment.
"Don't delay, screening saves lives - it saved mine."
Leeds Teaching Hospitals, which revealed the 12,000 figure following a Freedom of Information request, said most of the women have now been offered a new date for screening.
Dr Nisha Sharma, director of breast screening and clinical lead for breast imaging at Leeds Teaching Hospitals, said: “It’s really important that women are aware that the breast screening service is fully operational, that it’s safe to attend and that we are running additional sessions across the weekend to fit as many women in as quickly as possible.
“During the first few months of lockdown in March 2020, the Leeds/Wakefield breast screening programme was paused, but since the end of June we have continued to deliver breast screening without any interruptions to the service, working within Covid guidelines and guidance.”
Baroness Delyth Morgan, chief executive at research and care charity Breast Cancer Now, said: “The NHS breast screening programme has faced substantial disruption due to the Covid-19 pandemic, with services being paused for several months last year and appointments now running at a reduced rate due to safety measures.
"Breast Cancer Now estimates that in 2020 nearly 1.2 million fewer women across the UK had breast screening as a result of the pandemic, and the stark reality is that some women with breast cancer may not receive an early diagnosis, which is critical to stopping women dying from the disease.
“The NHS has been working tirelessly to restart and deliver breast screening services, however, the growing backlog of women waiting for an appointment is placing immense pressure on a diagnostic and imaging cancer workforce that was chronically over-stretched even before the pandemic.
"A fully resourced breast cancer workforce is urgently needed and it is vital the Government provides significant investment to enable the breast screening programme to make a swift recovery and to be sustainable – to give all women, now and in the future, the best chance of survival.
“While screening comes with some risks to be aware of, it is a key tool in the early detection of breast cancer and we encourage women to attend their breast screening appointments when invited during the pandemic, and to also get in touch with their GP if they find any new or unusual breast changes.
"When attending an appointment, safety measures will be in place to reduce the risk of the spread of the COVID-19 infection. Anyone seeking information and support can speak to our expert nurses by calling our free Helpline on 0808 800 6000.”
Nicki Embleton, Cancer Research UK’s spokesperson for Yorkshire, said: “Covid-19 has had a devastating impact on cancer services, including screening programmes.
"We estimate that between March and September 2020, around 3 million fewer people in the UK were screened than in the same time the previous year.
“Cancer screening has restarted across the UK, but there’s now a significant backlog.
"It’s vital that people who missed out on cancer screening are invited to take part and given any follow up tests needed as soon as possible.
"If you notice any unusual changes for your body, don't wait for your screening invite - contact your GP. Early diagnosis can make all the difference.”