Tim Hardin – Eulogy to Lenny Bruce
Belle & Sebastian – Roy Walker
REM – Man on the Moon (Andy Kaufman)
REM – It's The End Of The World As We Know It (Lenny Bruce again)

...is mentioned in Give Peace a Chance, of course.

by Bob Dylan

That Style Council one with Lenny Henry doing the spoken word part.

(That´s a proper song title, isn´t it?)

Harpo, Groucho, Chico + Woody Allen :Reasons to be Cheerful, Part 3 -Ian Dury and the Blockheads

Cannon & Ball :Thats What I Like -Chas 'n' Dave

Namechecks more celebs than probably any other song (Unless you know better?)
Comics include :
tommy cannon and bobby ball
barry humphries
leslie crowther
mork and mindy (from comedy tv show)

Any other song name more??

As it's a 'list' song, but Cannon & Ball also mentioned in Hello by The Beloved

As is Barry Humphries...

[edit] 2 minutes too late!

The Human League's The Things That Dreams Are Made Of:

“New York, ice cream, TV, travel, good times
Norman Wisdom, Johnny, Joey, Dee Dee, good times”

And Leonard Rossiter makes it into the list of the great and the good in The Skids’ TV Stars.

... had a tune called Rodney King (Song For Lenny Bruce) which seemed a bit confusing.
And didn't both Tool and Radiohead dedicate albums to Bill Hicks? I could be wrong here.

not sure if it's been recorded but he used to play it live. It's on a Glastonbury '89 bootleg and there's a spoken word bit (by Georgie Fame) which goes (something like); "Spike Milligan, Peter Sellers, Michael Bentine, Harry Secombe, Arthur Askey, Norman Wisdom, Frankie Howerd, Norman Vaughan, Dave Allen, John Cleese, Terry Gilliam, Michael Palin, Graham Chapman, Eric Idle, Ministry of Silly Walks, Benny Hill, Harry Worth, Tommy Cooper, Just Like That, Max Wall." Then he does a list of snooker players.

...consists of a parade of singers on variety shows dressed up as Chaplin singing songs about him...but I can't actually remember any of these songs and they might not exist at all. Maybe they were singing about something else completely and just enjoyed dressing up like him and doing the wobbly walk.

Tommy C by Dan le Sac and Scroobius Pip

'Tommy Cooper was in the entertainment game

Every granddad in Britain can do a Tommy Cooper impression

With a selection of gags, hand movements and facial expressions

His uniform was a suit and a red fez hat

He would combine jokes and magic tricks "just like that"'

http://www.we7.com/#/song/Dan-Le-Sac-vs-Scroobius-Pip/Tommy-C

mentioned in this (2:55)

have a big hit with a song about the greatest comedian who ever lived?

I think it was was called Mull Of McIntyre

I'm sure I've got a cassette of it in my man drawer.

mentions Duncan "Chase Me" Norvelle *

*may not be true

namecheck Mr Pastry, Arthur Askey and Charlie Chester in Friends - which in turn was the inspiration for a popular US sitcom of the 90s.
I think Squeeze mentioned Morecambe and Wise in a Christmas song - possibly a B side?

Up On Cripple Creek

Now me and my mate were back at the shack, we had Spike Jones on the box
She said, "I can't take the way he sings, but I love to hear him talk"

...it came to mind anyway, so here it is: Ralph McTell's instrumental tribute to Oliver Hardy, 'That'll Do Babe' (here performed - rather well - by a Ralph acolyte).

And let's not forget the HJH's eulogy to Charles Hawtree on 'Let It Be'

Arthur being Arthur Askey

Won't You Come Home Bill Bailey?...

named after Bill Hicks' band, and written as a tribute to him, though it doesn't mention him by name.

...'Hooray For Harold Lloyd' written by Neal Hefti sometime in the 70s for TV comps of the silent maestro's ouevre

Thanks everyone for such a great response so far. Really enjoyed reading it all. I thought there must be a few songs about for Lenny Bruce but had no idea that Leslie Crowther, Leonard Rossiter or Cannon and Ball ever got a namecheck!