Newly appointed Home Secretary John Reid will not be granted a grace period from MPs demanding answers sacked Charles Clarke failed to address.
Bradford MPs have vowed to continue to push the new Home Office boss over the cases of Stephen Ayre and of Mustaf Jamma.
Twenty-five-year-old Jamma, wanted in connection with the shooting dead of PC Sharon Beshenivsky, avoided deportation just months before the Keighley mum was killed.
MPs have also backed the Telegraph & Argus's call for answers to key questions about how convicted murderer Ayre, 44, who was free on licence, was able to kidnap and rape a ten-year-old boy because he wanted to go back to prison.
Shipley MP Philip Davies, who repeatedly called for Mr Clarke's resignation earlier this week, said: "Just because Mr Clarke has gone it does not mean the problems have. I will keep pressing for answers until I get some.
"Mr Clarke has left behind a shambolic system. I do not hold out much faith that John Reid will provide the answers but he needs to get a grip of the situation very quickly."
MP for Bradford West Marsha Singh believes Mr Reid will be able to sort the problems of his new department.
He said: "He has a very good reputation and I am sure he will do a very good job. I will continue to press for a clear commitment to sorting out the issues and will be raising the Bradford cases again with him."
Yesterday the Labour backbencher said sacking Clarke was not enough and it was time for the Prime Minister to resign. He said: "The Cabinet reshuffle was long, long overdue but it just doesn't go far enough.
"Everybody knows that Tony Blair is on his way out. He should go now.
"It's time for the leadership of the party to start connecting with the voters again."
MP for Bradford South and Government minister Gerry Sutcliffe said he was "very sad" to see his colleague Mr Clarke return to the backbenches.
He said: "Clearly there were issues that were unresolved and we hope we can now move on."
MP for Bradford North Terry Rooney said he would press Mr Reid for answers on the two cases: "The Bradford MPs will write a letter to Mr Reid addressing the two cases. I will certainly continue to push for answers."
But although MP for Keighley Ann Cryer said she would press for answers, she said if Jamma was in Somalia he should remain there.
She said: "If he comes here and is tried and goes to prison, we will again face the problem of deporting him. Do we really want him back here?
"I will press Mr Reid over deportation regulation and also suggest life-long tagging for people like Ayre.
"I am sure I will come up against the human rights lobby but there is a great problem he needs to address."
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