Swiss pharmaceutical company Roche said problems with a move to a new warehouse had led to a "very significant drop” in its processing capacity. They have warned could take two to three weeks to resolve.
Concerns have been raised over the supply of vital testing materials for a range of conditions, including Covid-19 and cancer.
The company also provides materials for a wide range of procedures including blood and urine tests, as well as diabetic care.
But International Trade Secretary Liz Truss told Sky News: “There is an issue with the supply chain. Roche are working with the NHS, the Health Secretary is fully aware.
“I would encourage people to continue going through the testing process – that process is still working.
“Testing continues, people should still – if they have symptoms of coronavirus – put forward for the test.”
She said they were pushing hard to resolve the issue, adding: “As soon as this issue identified by Roche, it’s been flagged to the Department of Health. We are dealing with it.”
In a letter seen by the PA news agency, the company told customers to activate their local contingency plans "and recommend that you look to prioritise essential services only".
It is understood the issue has not had an impact on Covid-19 tests at this point and the company is prioritising the dispatch of Covid-19 and antibody tests.
A Roche spokesman said: "We deeply regret that there has been a delay in the dispatch of some products and apologise to any of our customers who have been impacted.
"As well as extending working hours, we have recruited extra staff and, where they can, our dedicated teams on the ground are working with customers to distribute products and minimise service disruption.
"We will continue to provide regular updates to our customers and we are doing everything possible to return to routine operations.
"We are prioritising the dispatch of Covid-19 PCR and antibody tests and doing everything we can to ensure there is no impact on the supply of these to the NHS."
An NHS spokesman said: "Roche has alerted hospitals to an issue with their supply chain, and they will be working urgently to resolve this issue."