“Combined with the success of the HPV vaccine for both boys and girls, we hope that cervical cancer can be eliminated altogether by the NHS in England. The chances of surviving cancer are at a record high, but there is always more we can do, as we continue to deliver our long-term plan.”

The NHS believes 600 cases of cervical cancer – roughly a quarter of the 2,500 cases detected in England – could be prevented by the new HPV screening test.

As the generations of young women given the vaccine get older, the numbers of cases of cervical cancer are expected to drop substantially. Australian academics writing in the Lancet medical journal last year estimated that comprehensive vaccination and screening could bring the caseload down to fewer than four in 100,000 women, a level at which the cancer would be considered virtually eliminated. The UK rate is just below 10 per 100,000.

Vaccination is expected to make a big difference to the chances of girls and women in low- and middle-income countries that have the most cases and where there are no routine screening programs.

Experts are enthusiastic about the prospects. Robert Music, the chief executive of the campaigning charity Jo’s Cervical Cancer Trust, said: “It is exciting that we are seeing advances in cervical cancer prevention and must continue to look to the future to make sure our cervical screening program continues to adapt and evolve.

“The day that cervical cancer is a disease of the past is one we should be aiming to get to as soon as possible. Cervical screening is such an important test, but there are many reasons it can be difficult to attend. We must continue to understand and tackle these to ensure as many women benefit from this far more sensitive test and we save as many cancers diagnoses and lives as possible.”

Prof Anne Mackie, the director of screening at Public Health England, said: “With HPV vaccinations for all year 8 pupils and HPV testing available nationally, cervical cancer promises to become very rare indeed. This is a truly momentous achievement, but to ensure we consign this disease to the past we must keep vaccination rates high and continue to provide safe and acceptable screening for all women.”

Jo Churchill, the public health minister, encouraged all women to continue to be screened. She said: “Thousands fewer women will be diagnosed with cervical cancer as a result of improved screening services and the HPV vaccine and it’s incredible to think that cervical cancer could be eradicated for good.

“The NHS long-term plan has committed to an overhaul of screening programmes, new investment in state-of-the-art technology and a boost in research, which will help more people survive cancer each year. I encourage all women to attend screening appointments.”