On the other hand, I am a great fan of Karl Barth, whose methodology is often thought to be the exact opposite. For Barth, although the events to which the New Testament bears witness did indeed occur in history#, in their character as revelation they are emphatically not available to all. Revelation, for Barth, is always God's action. He talks about it as a door, which can only be opened from the other side - i.e., God's side. The historian, qua historian, has no access whatsoever to this.
Second, the historical investigation "must really be impartial." That is to say, it is no use if the historian has already decided what can and can't happen in history, or what is to qualify as historical knowledge. Impartiality means at the very least hearing the texts on their own terms. (And not, for example, ruling out their witness to the resurrection because resurrections don't happen, or designating such witness as beyond the scope of historical enquiry because dealing with matters of faith rather than history).
Polar opposites?
Well, actually, no. Wright does take fairly regular pops at Barthians in TRotSoG, but he is usually wisely careful to blame the followers and not the master. Some followers of Barth have certainly ended up in what is basically a Christianised existentialism, where the history of Jesus is basically inaccessible and we just have to take a leap of faith into the (hopefully) waiting arms of revelation - but that isn't Barth's position.
In three paragraphs (Church Dogmatics IV/2, 149-150), Barth summarises his position on the historical accessibility of knowledge of God through Christ. "Is there", he asks, "a 'historical' knowledge of this event" - he is speaking of the event of revelation, by which he means specifically the life, death, and resurrection of Christ - "which can be maintained neutrally and with complete objectivity?" The first answer is 'no', not if we're talking about real knowledge of God, which necessarily overflows in love. That sort of knowledge - we might call it relational knowledge - can of course never be objective in that sense, nor is it in any way neutral. And for Barth knowledge of God is necessarily relational knowledge. So, no, if we're talking about "knowledge in this decisive sense", there is no generally available historical revelation.
But... "neutral and objective - 'historical' - knowledge is its presupposition".
In other words, historical knowledge is necessary, but not sufficient, for relational knowledge.
He offers two clarifying statements. Firstly, this historical knowledge will mean "the most impartial and painstaking investigation of the texts which speak of this event." To try to go around the New Testament and its witness is not to seek historical knowledge of these events, but to import one's own understanding. To seek historical knowledge of an event without reading the texts which witness to this event - well, its sufficiently nonsensical to call into question the motives.
Second, the historical investigation "must really be impartial." That is to say, it is no use if the historian has already decided what can and can't happen in history, or what is to qualify as historical knowledge. Impartiality means at the very least hearing the texts on their own terms. (And not, for example, ruling out their witness to the resurrection because resurrections don't happen, or designating such witness as beyond the scope of historical enquiry because dealing with matters of faith rather than history).
I think Barth is absolutely in agreement with Wright here; the difference of emphasis between them is complementary and not contradictory. In TRotSoG Wright effectively endorses this perspective. Historical investigation can lead us to the conclusion that the most reasonable explanation for the rise of the church is the empty tomb and the physical resurrection of Jesus from the dead. It cannot get us from there to God. But surely knowing historically that Jesus rose is the essential presupposition for seeing in him the revelation of God.
Some 'Barthians' I know would object that this is to put the Word of God on trial. If God has spoken to us, then we should receive his Word and not question. I agree, but it seems to me that what God has said, he has said in history. His Word is the life, death, and resurrection of Christ. To hear that Word in faith is more than, but it is absolutely not less than, to hear it in history.
* I don't think the enormous fourth volume, on Paul, is quite so good, although there's a lot of valuable stuff in there if you have the time to search for it and the strength in your arms to lift the book.
# If you have ever been told that Barth did not believe in the historicity of, say, the resurrection of Jesus - well, that is just plain wrong. It can only be maintained through either ignorance or reading and reasoning in very bad faith. But that's another topic for another day.