Dr Justin Varney, from Birmingham City Council’s public health department, said: “This… prevents family members providing childcare, and that is having significant impact on lots and lots of families.”
West Midlands mayor Andy Street warned people they must comply with new restrictions or face even tougher measures.
“We will use these restrictions, look at how the numbers move, and if they are not sufficient, we might have to go further,” Mr Street said on Sunday.
“Everybody now has to comply with these to give us the best chance.”
Under the new rules, people are banned from meeting others who are not in their household or support bubble, indoors or in private gardens.
People can still go out to shops, restaurants and other venues, in a maximum group of six from more than one household, but the council told people to be “vigilant”.
West Midlands Chief Constable Dave Thompson said he understood it had been a “tough time”, but urged people to act responsibly.
He said officers would aim to “educate and encourage compliance” with the restrictions and would focus efforts on “disrupting flagrant breaches, such as large gatherings”.
Figures show the rate of cases per 100,000 in Birmingham to the week to 11 September was 82; for Solihull the figure was 71.2; and Sandwell stood at 64.2.