Well it's all coming together! We just got back from London, having spent 4 days walking practically every neighborhood between Marbel Arch and Stepney Green. We fell in love with one neighborhood: Angel (despite what some naysayers on this board said, we LOVED it). We immediately put down rental bids on two flats. Sadly both were rejected because the owners wanted somebody to move immediately and we can't come until August. Our search continues, but at least we've narrowed it down to a neighborhood.
But the point of our trip was not just to find a flat, but to find a neighborhood we loved and where we felt comfortable. That's something you cannot get sight-unseen from a tour book, realtor website or, as we discovered, even from fellow UK Yankees. It all comes down to personal preference, and one person's trash neighborhood is another person's treasure.
We also discovered that, as in the USA, you cannot trust what you see on a realtor's website. Some places we viewed looked great on paper on website. But the pictures on the website failed to mention downsides about the neighborhood. For example, one place we loved from the website failed to mention that the downstairs neighbor is a nightclub DJ who was blaring bass-thumping stereo all day long. Another site we viewed that looked great on a listing was directly across from an all-night discotecque. And still another was next door to council housing (i.e. public housing complex). And others over-inflated (read: LIED) about the measurements of the size of the flats.
It really is worth the cost to fly to London for a few days to find a place before you move. Most flats seem to go on the market 6 weeks before the owner wants it to be rented.