The resignation of Andrew Mitchell was the "right decision", a police representative has said.
Simon Payne, chairman of the Warwickshire Police Federation, told Sky News: "We've wanted to move on for weeks. This problem is not of our making, it's squarely at the Government's foot, and it's ended with a right decision, finally, which is the resignation of Andrew Mitchell.
"What we now need to do is clear the air, find out from Mr Mitchell what he actually said, and then we can move on to some more important issues which currently face policing in our country."
Paul McKeever, chairman of the Police Federation of England and Wales, said: "It is not good to see anyone fall from public office but the decision by the Prime Minister to accept Andrew Mitchell's resignation seemed almost inevitable. Andrew Mitchell has apologised to our Metropolitan Police colleague and our colleague has accepted the apology. We hope this matter is now closed."
Labour's shadow Cabinet Office minister, Michael Dugher, said Mr Mitchell should have resigned earlier.
"After weeks in complete denial, Andrew Mitchell has finally bowed to public pressure. What people will want to know is why, when the entire country could see that what Andrew Mitchell did was wrong, the Prime Minister totally failed to act," he said.
Nick de Bois, Conservative MP for Enfield North, told the BBC: "Andrew has made the right call, but I feel a lot of sympathy, he's been through a very difficult time. I think he probably recognises that this had become a very toxic issue which was not allowing the Government to remain focused on its priorities."
Mark Pritchard, Conservative MP for The Wrekin, said: "Andrew Mitchell is probably the best Development Secretary this country has had since Lynda Chalker. A lot of people are alive around the world because of the programmes led by Andrew Mitchell, so that's a huge legacy.
"We all get frustrated, police officers get frustrated, police officers swear at the public, and I think Andrew Mitchell has paid a very, very heavy price for being frustrated after a long and frustrating day."
There were questions to be answered about how police log books found their way into certain national newspapers, Mr Pritchard said. "There are questions to be answered about the relationship the police still appear to have with the British media."