Where to buy vinyl in London?

I'll be traveling to London for the first time ever next month and have a couple of days to spend. Do you have any recommendations for vinyl shops in London? Given the location, English pop rock and new wave 60's - 80's would be great. Modern European indie, jazz and dance music, or just a good overall vinyl store...

I've searched this site and all of the posts were many years old.
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Pick up a copy of the Record Collector magazine . It is published in the UK and has a very extensive listing of record shops. Barnes & Noble is where I buy my copy.

Berwick St, formerly the most famous in the land for music shops, very close to Oxford Circus : Reckless/Revival Records and Sister Records (mentioned earlier?) are the only survivors.
Although I'm not local, I was there scanning the shelves only a few weeks ago.... :)

Also visited a place called "Rat Records" in Camberwell (on the Southern side of the Thames 1 mile from the Oval Tube station)
Hope this helps....
Thanks, folks. I'm staying in Shoreditch, and looking forward to a little vinyl hunting. Will also check out Ronnie Scott's when I'm there.
old request but updated answer Music and Record exchange in Notting Hill Gate and Rough Trade Records in Notting Hill.
All of the old favorites seem picked over or mostly new print and new releases.

I was at M&R exchange last night and was able to find some goodies.  Their rating system is accurate too.