He said NHS trusts are "working in the dark", unaware of why the shortages are occurring, how long they might last, how widespread they are, and what priority will be given to healthcare workers and their families in accessing scarce tests.
Now in the United Kingdom anyone with coronavirus symptoms can get a free test via the National Health Service, but a spike in the number of people wanting to get tested has seen long lines outside testing centres and reports of people in England's 10 worst-hit COVID-19 hotspots unable to get any tests at all.
Chris Hopson told Sky News television there were "current capacity problems with the testing regime", and urged the government to prioritise frontline health workers.
Home secretary Priti Patel said it was "unacceptable" that some people were struggling to get tests, and "much more work needs to be undertaken with Public Health England".
"We are in for a rough few weeks", one source told the Times, as hospitals and care homes increasingly complain about the insufficient amount of testing kits they receive.
"Throughout this pandemic we have prioritised testing according to need", he said.
Britain's health minister said on Tuesday that the government was working around the clock to fix what he said were "operational challenges" in the novel coronavirus testing system caused by a surge in demand.
"So, for them that's a real problem".
Because of the surge in demand for tests, the United Kingdom government has promised to increase capacity and urged people only to get a test if they are showing symptoms.
"Our latest survey showed how concerned the trust leaders were about the effect of insufficient testing on their ability to restore services, and it is disappointing that no detailed information on current problems has been shared", he said.
She added: "Our members, and especially in general practice, are concerned that their staff are having to self-isolate unnecessarily due to delays and difficulties in access to tests for themselves and their families - and that some are having to wait longer than expected for the results - which is putting a strain on the services they can provide".
The Government said that as of 9am on Tuesday, there had been a further 3,105 lab-confirmed cases of coronavirus in the UK.
- Former health secretary Jeremy Hunt said constituents in his Surrey constituency had been sent to Bristol or the Isle of Wight for tests.
"I must say I burst into tears".
On reaching the test site, he was told he could not get the test.
In the end, he applied for the first test appointment he could find anywhere in the country - in this case, about 500 miles in Dundee - and managed to get a QR code.
A Government source said that while hospital admissions for Covid-19 are now at a low level, they will rise as infections rise across the community.
Mr. Hobson called on the government to "be honest and open" about what was going on. "I welcome enormously the return of children to school but. this has led to a very large increase in the number of children who are being sent to testing centres, often bringing their parents and other household members with them, and that has put an enormous pressure on the system", he admitted. "Down here on Planet Earth, we need a fit-for-purpose test and trace system in the here and now".
Mr Hancock said he would examine the issues raised.
A new laboratory will also open near Loughborough in the coming weeks, which will be able to process 50,000 tests per day.
Hancock insisted that capacity for testing was "at a record high" and 9,278 tests were carried out on Monday in the 10 areas of the country worst-hit by a surge in cases.
An NHS spokeswoman said: "Hospitals continue to fully comply with recommended patient and staff testing protocols".
"So extra demand on the system was inevitable, so why didn't he use the summer to significantly expand NHS lab capacity and fix contact tracing?"