The Government hopes to have capacity to test 25,000 people each day for coronavirus by mid-April.
As pressure mounts for more widespread examinations, housing secretary Robert Jenrick said capacity at present had reached 12,750.
He told Sky this was "clearly not as much as we would like".
Asked when the target of 25,000 per day would be reached, he said: "We'd like to be at that position by mid-April."
Mr Jenrick also said that the capacity now gives a position for NHS staff to be tested, which they had previously been unable to despite exposure risks.
Some of those workers will also be able to do home tests, he added.
As well as comments on testing, Mr Jenrick was also pressed on ventilators.
He said that the Government had received 30 new ventilators from British manufacturers who started making them due to the coronavirus outbreak.
"I appreciate that's a small number but that's just the beginning," he said.
Mr Jenrick would not comment on exact figures of how many there would be in a week's time though said there was hope of thousands more.
He said the UK currently has 12,000 ventilators.
His comments come in the face of growing pressure to up examination levels.
The World Health Organisation has urged nations to "test, test, test" while other European countries have tested hundreds of thousands of citizens.
Healthcare professionals have backed the call while Labour leader Jeremy Corbyn also raised it as a priority.
