The tests could waste scarce NHS resources, a group of senior academics is warning.
Over the coming weeks, 300 healthy people will each be given two doses of the jab.
A Labour Party analysis of NHS England figures revealed the growing backlog.
The warning comes as the prime minister announced sweeping relaxations to lockdown rules in England.
They also told US lawmakers that they had never been asked to slow testing for coronavirus.
Data shows significant drop in the number of emergency contraception sales amid Covid-19 lockdown.
A spike in cases in North Rhine-Westphalia has led to reimposed lockdowns in two state districts.
Tens of thousands of people will need to be checked to see if they have permanent damage, doctors say.
Experts are investigating whether coronavirus could have been passed through the mother's placenta.
The NHS is calling for men who have been ill with the virus to donate blood for treatment trials.
The first of a new family of drugs to stop cancer cells from repairing themselves has been trialled.
Professor Peter Piot, one of the world’s top infectious disease experts, was hit by Covid-19.