Prime Minister Theresa May has vowed to trigger Article 50 of the Lisbon Treaty by March, setting the ball rolling on two-years of negotiations to set the terms of the divorce.
Trade and immigration are set to be the key issues, with European leaders saying they will not compromise on open borders within the bloc.
Brexit-supporting MP Andrew Bridgen accused Verhofstadt of trying to sow division in Britain.
"It's an attempt to create two classes of UK citizen and to subvert the referendum vote," he told The Times.
"The truth is that Brussels will try every trick in the book to stop us leaving."
Former British prime minister Tony Blair, who is pro-European, this week argued the UK's exit from the European Union could be stopped.
In an interview with the New Statesman, the former Labour leader suggested voted had the power to decide if the pain of leaving the world's biggest trading bloc outweighs the benefits of leaving.
"It can be stopped if the British people decide that, having seen what it means, the pain-gain cost-benefit analysis doesn't stack up," he said.
"I'm not saying it will (be stopped), by the way, but it would. I'm just saying: until you see what it means, how do you know?"
The June 23 Brexit vote took many investors and chief executives by surprise, triggering the deepest political and financial turmoil in Britain since World War II and the biggest ever one-day fall in sterling against the dollar.
While most British politicians agree the referendum result means a divorce must happen, some EU leaders have openly speculated over whether Britain might reconsider the divorce.
But May has repeatedly said: "Brexit means Brexit."
- With AFP