In London you're never more than 6ft away from a celebrity. Something like that anyway. It certainly seems Londonist readers have had their fair share of celeb run-ins.
Feel free to add your own to the comments at the end.

Right royal run-ins
Saying "good afternoon" to Princess Diana in passing on Hampstead Heath... - Anthony Moriarty
I shook hands with Prince William and Prince Harry outside Clarence House the day before the royal wedding! - Vic Diana
I was in my old style Austin Mini and saw the Queen in her car smiling at me in a Mini! - Gareth Jones
And (literal) political run-ins
Red faced puffy cheeked David Cameron PM jogging (pounding) towards me and my daughter in Green Park - Stephen
Danny Alexander. Waved at me like he had strings attached and we were old friends. - Emma Pentland
Maria Miller walking towards Downing Street to hand in her resignation as culture secretary. - Tom Purves

Not bad Beatle encounter
I crossed Oxford Street next to George Harrison once. We didn't acknowledge each other. - Carole Fonten
Amazing Beatle encounter
Paul McCartney sang me happy birthday in a little restaurant in St John's Wood. - Jeff Wolfers
A slightly less famous singer
Remember Lulu? I was behind her in line at the bread counter at Selfridges in the 70s. She bought challah and said to her friend "I just love that Jewish bread." - Carole Fonten

Being nice to celebs
I helped Kate Bush once in Cabaret Mechanical Theatre, Covent Garden... She was tiny. - David Blackburn
Marco Pierre White asking me for a light - Liam Paton
And more cigarette favours...
Back in the very early 80s I met Lemmy in the Ladbroke Grove/Portobello Market area. It was about midday and he was off his face. He saw my Motorhead t-shirt and blagged a handful of Marlboro off me. He was very grateful and as I was fan of Motorhead he invited me to go to a party he was attending later that evening. Sadly, I was previously engaged and couldn't go but I always reflect what might have happened had I taken up his kind offer. Ahem. - parkylondon

And be careful who you're rude to. It might turn out to be your idol...
My partner obliviously shoved Neil Tennant out of the way on the stairs in the Curzon cinema. He's a massive Pet Shop Boys fan, and was gutted when, open mouthed, I told him what he'd just done. - Alex Evans
Although it can be cathartic to annoy some celebs...
[At a pub in Hammersmith] James May saw the morris dancers gathering at the front, and rushed to the beer garden at the back. "Not watching the morris dancers?" asked a regular "Actively running away," replied James May.
On another occasion one of our number did get him to grudgingly put a pound coin in the hat, but only because we were dancing in the road, and he couldn't get his car past until we'd finished. - Christopher Luxford
Last week I saw Boris on the tube and I gave him a piece of my mind - George Koutroukis

When you feel like you've stumbled into a Woody Allen film...
Diane Keaton — last week, in the Tate Switch House shop, asked me where the queue was... I said I wasn't sure, modern art can be very confusing...I thought it was funny...I know, I know... - David Blackburn
A gallery encounter of a different kind
I met JMW Turner in The National Gallery, fell instantly in love and have been seeing him regularly ever since. - George Mulrooney

Properly strange encounters
Boy George and Steve Strange, sitting under the sinks in the ladies at an Oh Boy Xmas party around 1976. Both giggling like schoolgirls and dressed in old WW2 uniforms, while asking to borrow make up from everyone who walked in. Nobody had a clue who they were then. A year later, same magazine Xmas party, I got in the lift and was grabbed and snogged by Billy Idol. He stopped when the doors opened, walked out without a word and was gone...weird. - Beverly Henry
And there's that Boy George again...
I got an air kiss from Boy George in Leicester Square. - Chrissy Carini
Seriously, what is it with Boy George?
Boy George buying fudge at the Duke of York Square food market - Suyai Ehlers

Boozy run-ins
Worked as an electoral canvasser and found Pete Doherty. He was wasted. I took his photo. Strangely he asked to take mine. - Jacqueline Smith
I was served by Amy Winehouse at the Hawley Arms. Oh, and I accidentally tripped up Prince Harry in the Roof Gardens last year. - Ben Smart
Drinking at a free bar with Frank Kelly (Father Jack) and the rest of the cast at the London Studios just after finishing the last episode of Father Ted, and bragging online the next day about having just partied with Dermot Morgan whilst arguing with all the idiots who kept saying that he had died. Until I saw the news for myself. - Philip Quinton

Should celebs be allowed to drive?
Ray Davies tried to run me over in a small orange car in Highgate - Alex Evans
James Nesbitt almost running me over in his bike. (He's speedy) - Tor C Drums
Claudia Schiffer almost ran over my wife and kids... - Room_237
Although it does seem to be two-way traffic...
I once nearly ran over Felicity Kendal on Drury Lane. She stepped out from between two parked cars... - Eileen Fox
When you're left speechless...
Walked past Jonny Greenwood at Old Street station days before Radiohead launched the new album. Couldn't speak for 10 mins. - Maria Nazdravan
My daughter and I were walking around London and all of a sudden she stopped and would not move. Finally she uttered, "Dumbledore!" She is a huge Harry Potter fan. She could not even move so I literally grabbed her arm and pulled her toward him so we could get a picture. Honestly I've never seen her speechless before! It was hilarious! He was very kind and let me get a picture of them. - Jane Romeo
Once I collided with Richard E Grant and was so starstruck I couldn't talk. He thought he'd hit me hard and got really worried. - Liz Sinclair

That Richard E Grant gets about...
Walking straight into Richard E Grant and proclaiming "Fuck it's Richard E Grant" to which he replied, "Yes, yes it is" - Kevin Mar
Er, are you sure this wasn't a dream?
At Gerry's in Soho circa 2001: Burt Kwouk practically crying into his pint on the table in front of me while Keith Allen got pissed on the table to my right and Alex James sat sulking on the table to my left because Keith Allen owed him a grand. Then Bjork came down the stairs with a couple of hard bastard bouncer types looking absolutely furious and sat in the far corner for half an hour before disappearing through some internal door. And all the while that short, balding fella from Auf Wiedersehen, Pet cracking jokes and coming across as a bit lonely. - Philip Quinton

This sounds rather unreal too...
The Hoff, In all white loose linen, at the top of a staircase framed by the low afternoon sun. No word of a lie. - Gabriel Lloret
You think it's all over...
I bumped into Geoff Hurst twice with years in between. I am not sure what the odds are of bumping into the same celeb years apart in different places in London. I was hoping to bump into him again so I could call it a Geoff Hurst hat-trick. - Gregg
Any celeb counts in this game
Gail Tilsley from Corrie walking down the King's Road in the 80s, Jason Donovan's dad at a bar in Portobello Road in the 90s and Tom O'Connor at a cinema in 1979 watching the movie Zulu Dawn. - Stephen Hofmann