A survey by the Royal College of Nursing also revealed 1 in 18 agency nursing staff have not even been offered a single dose.
Quizzed by Labour's Keir Starmer, PM says some of taxpayers' cash went on countering anti-vaxxers.
Tory peer defends use of private sector in creating "a retail organisation" bigger than Asda.
The government has been accused of putting "profiteering and corporate greed" before public health.
While many in the arts and culture sector have welcomed the injection of cash, others say it has come too late.
The project with private sector labs comes amid growing criticism over the lag in checks, with just 2,000 NHS staff tested so far.
Working with private sector contractors can leave you open to "ransom" and "gouging", he said
The private sector is hugely powerful. Many corporations have an annual turnover that dwarfs the budgets of national governments
Would Corbyn and McDonnell be as free market as Blair and Brown? No, but there's much for business to like in the party's economic plans
IVF Couples Being Charged Thousands For Unproven Treatments Is A Worrying Indictment Of The Private Sector
If the move to the commercial sector, which is so advanced in reproductive medicine, is indicative of life outside the NHS then I, for one, hope that we can protect it for as long as possible.