Sadly the largest music store on Oxford street HMV has shut down years ago, they used to stock a lot of hard-to-find and ambient CDs. It is now replaced a by a much smaller store that is not worth visiting. The HMV branch at Westfield shopping is a better option for CD. Fopp at Covent Garden is worth a visit.
For Vinyls you have Rough Trade Records, I recommend the one on Brick Lane. Not sure if Music Exchange is still good, though they mostly sell second hand.