Michael Gove told Andrew Marr that the “number of people being tested is higher than ever before. 300,000 tests were administered on Friday.” This figure was the total number of tests conducted, not the number of people tested. At the time, the government didn't publish figures on the total number of people tested each day. The total number of people tested will have been lower than this figure, as some people are tested more than once - Public Health England recommends that labs test borderline positive cases a second time.
We don’t know how many tests are being carried out on average for every person tested, because the government didn’t publish these figures.
It is interesting to compare the language used by Michael Gove about testing, with the language used by Rishi Sunak. Michael Gove was more careful with his words and did not utter an untruth, though his comments arguably risked misleading ordinary television viewers about the number of people tested. For instances of more misleading comments on testing data by Johnson and his ministers, see here, here, here, here, here, here, here, here, here and here.