Comment 2 by AtheistEgbert :

I don't know where this fantasy came from, that we are traditionally tolerant.

MacCulloch presented this issue by stressing that tolerance was relative. E.g. there was a time when NOT burning someone at the stake for heresy was the height of tolerance. He didn't shy away from detailing all the intolerance that went before the various baby steps towards tolerance but he did focus a great deal on religious tolerance - first of non-anglican protestants, then other christians - and skimmed over the wider social changes that most of us would consider the mark of true tolerance.

I found the series interesting and well argued for the most part, right up to the point the OP highlights where MacCulloch presents the CofE as some kind of panacea for social ills. Even then, to be fair, the CofE he describes in this role is an almost non-religious (or perhaps pan-religious) one. He seems to suggest that it should be a broad church in the very broadest sense. He failed to examine the logical step of people moving beyond religion but he at least seemed to favour the church adapting to a changing society rather than digging its heels in and reverting to fundementalism.