Boris Johnson has urged people to get a coronavirus test before they visit elderly relatives over Christmas.
However, health officials have said community testing may not be fully up and running until the new year.
Opening a Commons debate on the government’s new tier system for England, the prime minister said lateral flow tests were being rolled out across the country.
Asked by Liberal Democrat leader Sir Ed Davey whether tests would be available to anyone visiting family members over Christmas, he said: ”It is open for people to get a lateral flow test.
“In general, the testing system is available, at the moment, for people who have symptoms.
“But I would urge people who are worried that they may need to be in the company of those who are elderly or vulnerable to seek to get a rapid turnaround test.”
General Sir Gordon Messenger told a Downing Street press briefing that the nature of the scheme would vary “from region to region and from area to area” depending on local readiness.
“We are alive to the possibility that we will not be able to do this all at once, but we assess that local authorities are at varying levels of preparedness and readiness to do this,” he said.
“And therefore I can see this as an offer that will sequence over time and into January and beyond.”
Gen Messenger said that in deciding which areas to prioritise they would look at infection rates and at how long they had been living under tougher restrictions as well has how mature their plans for delivering the tests were.
Health secretary Matt Hancock had previously promised that all care homes would be allowed to have visitors before Christmas thanks to a further testing roll-out.
The Department of Health has today announced that more than a million tests will be sent to care home providers over the next month which will enable safe indoor visits.
Visits will be able to take place across all tiers, and the first visits will start on Wednesday, a spokesperson for the department said.
Mr Hancock said: “I know how difficult it has been for people in care homes and their families to be apart for so long. The separation has been painful but has protected residents and staff from this deadly virus.
“I’m so pleased we are now able to help reunite families and more safely allow people to have meaningful contact with their loved ones by Christmas.
“This news has been made possible by the unprecedented strides made in testing technology and capacity, as well as extra personal protective equipment (PPE) supplies.”