Nico Silins is responsible for the objections. (I'm responsible for any mistakes in presenting his objections.) It seems that we have a kind of unproblematic access to our evidence. Since our evidence is what we have to go on in forming a view without needing any prior reasons for starting here, perhaps we can say this:
AA: If p is part of my evidence, it is possible to know that p is part of my evidence from the armchair.
(1) Suppose we know E=K is true from the armchair.
(2) Suppose p is known to us by means of observation, but not from the armchair.
(3) p is part of our evidence [(1), (2)].
(4) If p is part of our evidence, we can know (3) from the armchair and without observation [AA].
(5) We know (3) from the armchair and without observation [(3), (4)].
(6) We know from the armchair that if (5) is true, p can be known from the armchair [E=K]
(7) We can know p from the armchair [(5)(6)]
But, (7) can't be right. (7) is incompatible with (2). Either knowledge is limited to armchair knowledge (i.e., the external world skeptic wins) or E=K is false.
Second and related objection (again, from Silins). Consider the transition from 'I know p' to 'I know p is part of my evidence', which is sanctioned by E=K and AA. Consider the further inference to 'My belief that p constitutes knowledge' from 'p is part of my evidence', which is licensed by E=K. It seems that I know that if my belief constitutes knowledge, it is not a Gettiered belief. Can I deduce from what is known when I know p is part of my evidence that my belief is not Gettiered? I doubt it.
Or, of course, AA is false. I think AA isn't quite right. The thing for Williamson to say (I think) is that access to evidence requires that the evidence is there to be accessed and given what evidence is, there's no reason to think that it can be accessed from the armchair. If the intuitive motivation for AA is just this: our evidence is what we have to go on in forming a view without needing any prior reasons for starting here rather than with something more basic, it seems to assume that we need something more basic than observational knowledge to serve as the start of our inquiry. But, what could justify that? Nothing promising comes to mind.
While I think that this is an initially promising response, there's an easy way to reinstate Silins' objection. Instead of AA, why not say this instead:
We need no more empirical knowledge to know that p is part of my evidence (when it is) than I need to know p
That seems to be the sort of thing that is congenial to W's view, but it also seems to allow me to reinstate a version of the second objection to W's account.
So far as I can tell, Silins' objections to W apply to my account of evidence only if we assume the principle of armchair access:
(ET) p is part of my evidence only if p.
(IKSE) If p is known non-inferentially to me, p is part of my evidence.
So, if I'm right and AA is false but the principle in bold is acceptable, (ET & IKSE) avoids a real difficulty that arises for E=K.