I went to Borderline on my last trip and felt like I was wasting a night, because the experience was just too similar to standing around in Iota. The one thing I thought was interesting about it was in the entrance where they have lists of every show that ever happened there. I'm sure there's a Grog And Tankard in London, but going there will be exactly like going to Grog And Tankard. And when it comes to the hotter Brit bands, you can often get better access here. That is, a good British band that plays theater or arena venues in England might be at a 930 or Black Cat here.
In contrast to the Borderline night, on the next night we checked out the cheapo chamber-music performance at St Martins In The Fields, which was awesome, ate at Belgo and then went to one of the huge Ministry Of Sound type clubs just for the spectacle of it. Sure that's staying right on the tourist track, but we totally enjoyed the whole night, even though I can't stomach discos here for one second. Just like footie, it's the enthusiasm people have for it that makes it fun there.
The CD shops in Soho are mostly on Berwick St, the best is called Restless or Reckless. As the other people said, you aren't missing anything if you skip it