Callback using lambda with closures

I'm trying to implement a callback which passes control from an Interrupt Service Routine to a member function on a c++ class. I thought lambdas and closures would be a convenient means of doing this, but I'm having trouble implementing it. Below is a simplified version of my code.

The issue I'm stuck on is how to store the "function pointer" to the "lambda".

class Gpio
{
  public:
    typedef void (*ExtiHandler)();    
  private:
    ExtiHandler handler;    
  public:
    void enable_irq(ExtiHandler handler_in) 
    { 
      // enable interrupt
      // ...
      // save handler so callback can be issued later
      handler = handler_in;
    }
};

class Button
{
  private:
    Gpio& pin;    
  public:
    Button(Gpio& pin_in) : pin(pin_in) 
    {
    };

    void button_pressed()
    {
      // do something
    }

    void init()
    {
      pin.enable_irq([this]() { this->button_pressed(); });
    }
};

Compiling fails with the following error message;

 no matching function for call to 'Gpio::enable_irq(Button::init()::<lambda()>)'candidate: void Gpio::enable_irq(Gpio::ExtiHandler) no known conversion for argument 1 from 'Button::init()::<lambda()>' to 'Gpio::ExtiHandler {aka void (*)()}' Build failed

How can I modify this code to resolve the compile error?