Hi pilota,
I'm a CFI in the US. Flew in California with an outfit called Pacific Coast Flyers in San Louis Obispo. If the sole purpose of your trip is to build time, this might be a good place to look, since the prices are a little bit lower on the central coast than in the LA or SFO areas.
To converting your license, I udnerstand that it is fairly easy. I had a brit come in and ask the same question not too long ago. According to the FARs, you basically just need a license, a current medical, to prove that you can speak and write english, and a translation of your licenses if appropriate. Which I imagine you won't need since yours are British. He said he went to the FSDO (Flight Standards District Office) and got it all done in about an hour.
Good luck,. .TFR