C++ Preventing const methods from changing data through a member pointer or reference

Say I have a simple class like this

class Foo
{
public:
    void foo()const
    {
        str[5] = 'x';
        x = 4;
    }
private:
    char *str; //some referenced data, not owned by Foo
    int &x; //references as well
};

This is valid because in the const method, its just the pointer itself that becomes const, not the data it points to. However in many cases that is not what I desired and I want a compile error if a const method tries to change these members contents (either directly or by calling a non-const method on that member).

Is there a standard solution to this?

I think some kind of wrapper class should be able to achieve this, and should also be something the compiler optimises out, although haven't sat down to try and design such a thing to cover all cases giving say a strong_const<char*> str and strong_const<int&> (also not sure on a good name...).