Director of testing Sarah-Jane Marsh said there is capacity at testing sites but laboratories processing the tests are at a “critical pinch-point”.
Ms Marsh added that the system is doing “all it can to expand quickly”.
There have been reports of people being told there are no appointments available at test centres in England and that there are no home tests kits available to send out.
Meanwhile, England’s chief medical officer, Professor Chris Whitty, warned that if people stop social distancing then “Covid comes back”.
In other developments:
– There were a further 2,948 lab-confirmed cases of coronavirus in the UK as of 9am on Monday, following the 2,988 reported on Sunday, which was the largest daily figure since May.
– Just over 57,400 deaths involving Covid-19 have now been registered in the UK, according to figures from official data sources.
– Aviation industry leaders have urged the Government to commit to a coronavirus testing regime for international arrivals, after a new regional approach to England’s quarantine policy was announced.
– A new Covid-19 cost tracker has been set up by the National Audit Office (NAO). The spending watchdog said that during the Government’s response to the pandemic, it had announced 190 measures, which have a total estimated cost of £210 billion. The NAO estimates the Government has so far spent over £70 billion.
Ms Marsh wrote on Twitter: “Can I please offer my heartfelt apologies to anyone who cannot get a Covid test at present.
“All of our testing sites have capacity, which is why they don’t look overcrowded; it’s our laboratory processing that is the critical pinch-point. We are doing all we can to expand quickly.
“We have additional NHS, Lighthouse, University and Partner Labs all due to open up imminently and we are also expanding the use of non-Laboratory based tests.The testing team work on this 18 hours a day, seven days a week. We recognise the country is depending on us.”
Andy Thompson, 38, a technical manager from Crewe, said his six-year-old daughter is home from school with a continuous cough, but has so far been unable to get a home test.
“It’s an absolute shambles. No home tests available. And now the nearest test centre is Oldham, a 100-mile round-trip with a sick child,” he told the PA news agency.
“I didn’t realise how bad it is. If you haven’t got a car, no way you’re getting tested.”
People have also complained in recent days and weeks of being directed hundreds of miles to get a test.
On Monday, Health Secretary Matt Hancock pledged that people would have to travel no more than 75 miles for a test.
Further problems with the testing system came as a member of the Government’s Scientific Advisory Group for Emergencies (Sage) said the latest increase in coronavirus cases is “very worrying”.
Professor Andrew Hayward said scientists are monitoring the data closely for signs of wider community transmission of the disease.
“Generally it is local outbreaks, but there is also very worrying increases in cases, particularly over the last few days,” he told BBC Radio 4’s Today programme.
“That is what we are really keeping a close eye on – the extent to which it moves away from these local outbreaks to broader community transmission.
“What we saw in the last few days from this surveillance data was this worrying increase in cases which, as we know from the first wave of the pandemic, can potentially get out of hand if we don’t be very serious about the control measures.”
It comes after Professor Jonathan Van-Tam said on Monday that the public had “relaxed too much” over the summer and described the rising number of cases as of “great concern”.
The deputy chief medical officer for England said: “This is a big change. It’s now consistent over two days and it’s of great concern at this point.
“People have relaxed too much. Now is the time for us to re-engage and realise that this is a continuing threat to us.”
Professor Whitty echoed the concerns, and wrote on Twitter: “We have, through the extraordinary efforts of the whole population, got Covid rates right down.
“They are now rising again, especially in those aged 17 to 29.
“If we stop social distancing, Covid comes back.
“We all need to protect others.”
Meanwhile, Mr Hancock told the Health and Social Care Select Committee problems with coronavirus testing capacity will be sorted within weeks.
When asked about Ms Marsh’s tweet apologising for people unable to get tests, Mr Hancock said: “We are working incredibly hard.
“We are doing everything we can. We have had these operational issues that I have talked about, we have had a problem with a couple of contracts and we discussed some of that in the House of Commons.
“But it’s a matter of a couple of weeks until we can get all of that sorted in the short term.”
He also told the committee of MPs that the first “credible” cases of coronavirus reinfection were starting to be seen.
“We have also just started to see the first credible cases of reinfection and through genomic analysis you can see it is a different disease to the one the person got the first time around.
“But in all the cases that I have seen it has been an asymptomatic second infection that has been picked up through asymptomatic testing.
“But the hard question is, because one of the most difficult parts of dealing with this virus is asymptomatic transmission what we don’t yet know is the transmissibility of the disease even from an asymptomatic person who might have had the disease before.
“But we have got a huge amount of work going into answering that question.”
Boris Johnson told his Cabinet that ministers must ensure there is “no complacency” among the public, and particularly young people, after a rise in coronavirus infections, Downing Street has said.
The Prime Minister and the Cabinet were updated on the Covid-19 response by chief medical officer for England Professor Chris Whitty and chief scientific adviser Sir Patrick Vallance.
Mr Johnson’s official spokesman said: “The Prime Minister cautioned that in other countries which had seen an increase in infections this was followed a number of weeks later by a rise in hospitalisations.
“The PM said that what had taken place elsewhere was that young people had gone on to infect older generations that had become seriously ill, and it was vital to ensure that did not happen here.
“The Prime Minister said the Government must remain extremely vigilant and ensure that there was no complacency from the public and young people in particular in following the guidance on how to prevent the virus from spreading.”