Coun Blake suggested the new Prime Minister was less enthusiastic about the effort to speed up growth in the North of England championed by former chancellor George Osborne.
Sacking Mr Osborne was one of Mrs May’s first acts after taking over from David Cameron.
In a speech, Coun Blake said: “I, like other northern leaders, have been genuinely concerned about the shift away from the Northern Powerhouse by Theresa May.
“I can assure you that as a northern Labour authority we’d certainly like May to distance herself from Osborne on lots of things - but the Northern Powerhouse isn’t one.
“Yes, much of Osborne’s work on the Northern Powerhouse was rhetoric. But Northern Powerhouse branding is liked by business and has traction abroad.
“With the Brexit vote, it’s important we don’t inflict damage on something that is helping regions outside London to attract international investment.”
Coun Blake was delivering a speech on English devolution in her role as the chairman of the Core Cities group of councils.
She also used the speech to blame the Government for the delays on efforts to agree devolution to West Yorkshire.