How does BUGB doctrine compare with the American equivalents? Which is it closer to? (The principle difference between the American denominations seems to be that the Southern Baptists encourage re-baptism while the American Baptists don't; the BUGB website doesn't seem to comment on this).
The BUGB is pretty liberal and there are many things on which it does not have a clear view. To that extent, I would guess it's a bit more like the American Baptists than the Southern Baptists who, from my transatlantic vantage point, appear to be more evangelical in their doctrine, generally.
Though there are some evangelical Baptist churches still within the BUGB, a large proportion of UK churches which bear the name "Baptist" are in fact either independent (in some cases affiliated with other independent churches through organisations such as Affinity, the Fellowship of Independent Evangelical Churches [FIEC] or the Evangelical Movement of Wales) or part of other Baptist denominations such as the Grace Baptists.