The Health Secretary has admitted there are "operational challenges" in the Covid testing system as he was summoned to answer urgent questions on the lack of availability.
Matt Hancock also revealed tests were now having to be prioritised and hinted rationing could happen in the future.
It comes as some people in the South East say it is 'impossible' to book a slot.
Much of the increase in demand is for children who need testing after being sent home ill from school.
Ashleigh Merriman from Sussex ended up doing a 350 mile round-trip to Wales to get a test for her son Oliver.
She says: "I can't believe there is nothing locally, this is going to be a real problem nationwide with coughs and colds and kids picking up germs and if there aren't tests, kids will be missing school unnecessarily."
Gill Jarvis from Bishops Waltham in Hampshire was told there was no testing available locally for her mother and father who are in their 80s.
She says: "Although the testing site are Winchester, Portsmouth, Fleet, we can't even when you phone they say there are no tests and when you put the SO postcode in you are told the nearest is Bury or Telford and it's not just my family this is happening to."The NHS is also worried about what happens if its staff struggle to get tests.
Saffron Cordery from NHS Providers says: "That's a real challenge because we need all hands to the pumps so we can recover the service and get it back to where it was before the virus."On Tuesday the Health Secretary acknowledged there had been increase in demand and said the system would have to prioritise those in most need.
According to some of those who did get tested on Tuesday in the South East, the best time to book an appointment is in the evening when new slots for the next day are released.