And he added: “I think that the public really understand what we’re trying to do here which is that, as a country, we need to continue to control this virus and the public have done an amazing thing over the past six weeks by using common sense, following the social distancing rules and bringing R [the rate at which the infesction is transmitted] right down.”
The government has also faced criticism over the fact that Johnson did not mention Wednesday as a return-to-work date in his initial Sunday night speech.
But the health secretary said: “Well I think that if that’s the biggest complaint that the Today programme has then I think things are fine.
“The truth is that people really understand the message.”
And he added: “People understand what 'Stay Alert' means – and people understand that together we need to control the virus and make sure that people follow the social distancing rules, but we are able to make some small adjustments that would just make life easier for people.
“For instance, being able to go out and exercise more than once a day is a really important change for a lot for people.”
"Absence of detail"
Writing in The Telegraph on Tuesday morning, former Tory leader William Hague warned the government against a reliance on “slogans“, amid a row with Scottish First Minister Nicola Sturgeon over the decision to replace the UK's longstanding "Stay At Home" message with "Stay Alert’"
And the ex-cabinet minister said: “I make no criticism of Mr Johnson for his broadcast on Sunday evening – he spoke well and clearly, the direction he set was right, and the immediate decisions justified.
“But he would be well advised in future to present a detailed statement to parliament first, with the accompanying documents and detail, and then address the nation.
“Then there would be far fewer opportunities for critics to jump on the absence of detail, or for the media to have to rely on briefings about the implications.”
Pressed on those comments, Hancock said: “I’m afraid that what matters is the substance of the changes.
“Whether the announcement was made to the nation on TV or to parliament - these things are all completely second order when we’re dealing with the biggest public health emergency in a generation.”