Shadow home secretary Yvette Cooper said Mrs May's announcement on Article 8 would do nothing to address the failings in the UK Border Agency which meant fewer foreign criminals were being deported.
"The truth is this Government is deporting fewer and fewer foreign criminals every year because of failures in enforcement and administration," she said.
"Drawing up new guidance for the courts is sensible, and Parliament will need to debate the detail. But it isn't enough to sort out the problem.
"The Home Secretary needs to get a grip of the Border Agency and address the fundamental reasons why too many foreign criminals are not deported."
More top news
The 13-year-old died in hospital after being hit in the back of the head by a bullet when his cousin fell of a hoverboard.
The psychiatrist brother of Chancellor George Osborne faces being struck off after admitting to an affair with a "vulnerable" patient.
Three men have been jailed for helping a 17-year-old join IS - after a trial heard one of them shared affectionate texts with the teenager.