ESA Headache
I think it unlikely, the requirements for (f) are extremely high and to be honest the problems that you describe in your post are unlikely to match this. One problem is that claimants are not required to complete the PIP activities pain free and the fact that they can walk further even while in pain will count against them.
The only exception to this would be if they could show that the pain was so severe, that despite their still being able to walk they should be considered as being unable to walk to a necessary standard.
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems 
