The Leader of the Commons, who himself was self-isolating last week while awaiting a test, said Labour MPs should stop complaining about the difficulties of getting one.
He told the House: “The issue of testing is one where we have gone from a disease that nobody knew about a few months ago to one where nearly a quarter of a million people a day can be tested.
“And the Prime Minister is expecting that to go up to half a million people a day by the end of October.
“Instead of this endless carping saying it’s difficult to get them, we should actually celebrate this phenomenal success of the British nation in getting up to a quarter of a million tests of a disease that nobody knew about until earlier in the year.
“That is a success of our scientists, our health experts and of our administration.”
It comes after hundreds of schools have had to partially or completely close due to the unavailability of tests.
Mr Rees-Mogg added: “Yes there is demand for more, yes demand exceeds supply but it is growing, the supply is increasing. And what has been done is really rather remarkable and something we should be proud of.”
He made the comments after shadow Commons leader Valerie Vaz questioned why the Government’s head of the coronavirus “Test and Trace” programme, Dido Harding, has not spoken in public since August.
Ms Vaz said: “Now I know that there is a health statement later, but where is the chair of the Test and Trace programme? She’s made no statement since 19 August.
She added: “So the number of tests returned within 24 hours has fallen from 68 per cent to 8 per cent – it seems to be all talk, talk and no test, test.”