where can I buy a rocking bird in the UK like Homer has in the episode
'King Size Homer'?

This retro toy is known by many names, including "Happy Drinking
Bird," "Dippy Bird," "Goofy Bird," "Magic Bird," and "Drinking Duck."
I've found several options for you in the UK.

"Not to be confused with smaller, inferior types or copies, this is
the full-size original type made by Arora in Taiwan, which is hard to
find here in the UK. Very collectable !

Brand new and tested, in original printed box with instructions.
This groovy chap is almost identical to those sold back in the 1960s
except that the quality of manufacture is now better! He's also just
like the one that appeared in 'The Simpsons'."

eBay: Happy Drinking Bird
http://cgi.ebay.co.uk/HAPPY-DRINKING-BIRD-The-classic-full-sized-version_W0QQitemZ6042645422QQcategoryZ30QQssPageNameZWDVWQQrdZ1QQcmdZViewItem

"Drinking Happy Bird
 New in original box
 Free Postage & Packing to the UK"

eBay: Happy Drinking Bird 
http://cgi.ebay.co.uk/ws/eBayISAPI.dll?ViewItem&item=6260877670&ssPageName=MERC_VIC_ReBay_Pr2_PcY_BIN_IT

eBay: Original Happy Drinking Bird
http://cgi.ebay.co.uk/Original-Happy-Drinking-Bird_W0QQitemZ6041221495QQcategoryZ30QQrdZ1QQcmdZViewItem

The Drinking Bird (ships internationally)
http://www.thedrinkingbird.com/?gclid=CLnh29Xu0oMCFRtpNAodvDM1_g

In case you're interested in learning more about the history of this
toy, and information on how it works, here are some interesting links:

Rotten: Dippy Drinking Birds
http://www.rotten.com/library/culture/novelties/dippy-drinking-birds/

OddStuff: Drinking Birds
http://www.backstreet.demon.co.uk/oddstuff/drinkingbirds/drinkingbirds.htm

H2G2: The Amazing Drinking Bird
http://www.bbc.co.uk/dna/h2g2/A640865

My Google search strategy:

Google Web Search: "drinking bird" site:.uk
://www.google.com/search?hl=en&q=%22drinking+bird%22+site%3A.uk

I hope this helps! If anything is unclear or incomplete, please
request clarification; I'll be glad to offer further assistance before
you rate my answer.

Please don't use the bird to operate a nuclear power plant. ;-)

Best regards,
pinkfreud

My dad brought me and my brother one of these each back from the Isle
of Man about 30 years ago.

We would put them in the kitchen window and pray for sunshine to speed
up the dipping process.  I used to love watching the bird(s) dipping
up and down.

Thanks for digging that memory up!

Try this Ebay seller (might be listed above too)

http://snipurl.com/ndv7

Please note that the eBay sale mentioned by murunbuchstansinger-ga was
cited in my answer (the second link).