The resignation of Andrew Mitchell has widely been seen as the right decision for him to have made, though he won sympathy in some quarters.
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."
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."
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.
Shadow home secretary Yvette Cooper said: "This is a sensible decision by Andrew Mitchell. It is very unfortunate that David Cameron allowed this to drag on so long rather than investigate and resolve it at the start. Letting it carry on like this sent a very bad signal to the police and public servants across the country about the Government's attitude."
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."