Maybe it was quite different in your neck of the woods, but I seem to remember that "famously bad June" actually being really good for the first two weeks (I was just finishing my first year at Manchester Uni during then so if it was good there, it must have been pretty fine for the rest of the UK!) - I think we all pretty much agree the rest of the month was awful everywhere.
July was good enough in London after June's decline continued into the first week, if a bit bland and being a slightly less sunny retread of July 96 without that month's hot spells, but it was at least warm and dry for the most part, mostly low to mid 20s.
August was the second hottest on record, with plenty of hot days exceeding 25C and a few surpassing 30C well into the second half (when we usually expect things to cool down), with no shortage of sunshine and I certainly don't remember much rain either, so I'm not sure how you could compare it to 2004.
And if you're including months that have summery spells (and some years have actually been warmer than some if not all of the so-called summer months), September was very decent, dry, settled and sunny, which after a series of distinctly cool and/or patchy Septembers was a precursor to the Septembers we have been spoilt with practically every year in the last decade (in fact since then I only remember 2000 being distinctly sub-par).
So all in all, that to me constitutes a pretty decent if inconsistent summer at least in the SE, although in comparing it to other good "non-classic" summers in the 90s, 1994 and 1996 fare better.
Incidentally, whilst we're comparing past Aprils to summers can anyone remember the stats/overall feel for April 1990? I remember it being pretty poor during on a fortnight trip to the Lakes a week before and after Easter (I think it even snowed around the 17th/18th on the ascent to Stickle Tarn) but then April 1984 seems to have been better than I remembered based on similar circumstances.