Where is the best place to spot celebs in London?

If you spot them, they're not likely to be anyone you've heard of - or want to. People who are desperate to be famous for being famous, on the other hand, may be inescapable in a variety of places, especially ones that aren't worth the inflated prices they charge - and that's if they let ordinary people in, in the first place.

Not that I'm cynical, or anything.....

Ok, I'll bite.
The places I've been to where I have seen so-called A-listers (and B and C listers) include:
Zuma http://www.zumarestaurant.com/zuma_uk.html
The Wolseley http://www.thewolseley.com/
The Fox & Hounds Pub http://www.thisislondon.co.uk/bars/r...-and-hounds.do
The basement cafe at Nicole Farhi http://www.nicolefarhi.com/restaurants/nicoleslondon/
The restaurant at Sotheby's auction house http://www.london-eating.co.uk/300.htm
TomTom coffee house on Ebury Street (good coffee) http://www.tomtom.co.uk/

We never went there to look for celebrities, that seems like a waste of time. And there's no guarantee you'll see anybody you'd recognize at any of those places.

Celebrity gawking aside, TomTom's coffee house really is a great place to go for coffee. That and The Wolseley remain my favourite coffee spots in London.
https://www.tomtom.co.uk/About/AboutCoffee.aspx

The Ivy, I always seem to see someone famous there (last time, some years ago, I had Alan Richman next to me and Alexander McQueen behind me). The Wolseley, as mentioned, is often a good bet and easier to get a table.

I often stumble across celebs just wandering the streets of Hampstead or West Hampstead(Jamie Oliver, Emma Thompson plus Helena Bonham Carter and Tim Burton several times)

Of course, you could always hang around the stage doors in the West End.

Or get tickets to the Graham Norton show:
http://www.sroaudiences.com/application.asp?show_id=330

I went a few times when the show had just started and they were actually pushing for people to come. Not so easy now.

The cafe at the major, Cotswold, branch of Daylesford Farmshop.

Though it's deeply unEnglish to notice any of them. Not just because they expect anonymity - but because anyone with any sense is too busy making a fuss of the Flannerpooch to pay any attention to talentless mediorities.