That reminds me of another band:
And also:
The Yardbirds. (Which is slang for “chicken.”)
Hmmm, I only am familiar with these phrases from lyrics to songs by other bands. Pink Floyd is too much of a stretch besides to hardcore octopus-lovers, but how about Ten Years After? Okay, maybe not 
I don’t think either should be in the list. It’s about food, not just stuff that you could eat. The rule should be something like “could you buy the stuff in a supermarket?” I’ve never seen dead people, cannibals, crow, dog, men, "rancid"s or goat for sale in such a place, not even Tesco Extra.
Gravy Train was an early '70s British progressive rock band, with similarities to Traffic, Rare Bird (is that another one?), and Jethro Tull.
Bees Make Honey was part of the London pub-rock scene of the early-mid '70s. I’m not actually familiar with their music.
The Cowsills
How about Sublime?
A Burning Water
Archers Of Loaf
Bass
Bass Hunter
Beans
Beatsteaks
Better Than Toast
Buffseeds
Cake Like
Candy Skins
Caviar
Cherry Monroe
Cinnamon
Damien Rice
God Lives Under Water
Goldfrapp
Hot Chip
Jimmy’s Chicken Shack
Junkfood
Lake Trout
Landon Pigg
Long Pigs
Loudermilk
Magnapop
Meat Beat Manifesto
Mighty Joe Plum
Octopus Project
Papas Fritas (in English this would be “French Fries”)
Pigface
Plumb
Refreshments
Sage Francis
School Of Fish
Seafood
Showbread
Sugarcult
Taco
The Appleseed Cast
Wheatus
I think we could do a spin off thread about things you might eat if you were hunting or starving. That one would have things like The Field Mice, Eagles and Stiff Little Fingers 
My thought was that Cannibals is definately a word related to eating and hense food, whilst Dead Kenedys hasn’t any food or eating relationship that I am aware of.
Maybe we should rejig this to just food available in any supermarket. So goat would remain (available in many Halal supermarkets) whilst removing many of the very obscure items and hidden food words, so bananarama et al will get the chop (pun intended) This is just to edit down the length of the list more than anything else.
It’s still huge, so I’ll kill off the drinks as well. Trying to keep it down to size.
Anyone who thinks something is removed incorrectly from the next list tell me, I know a lot about foods but far from everything.
Grant Lee Buffalo
The Mutton Birds (from New Zealand)
Kid Creole & the Coconuts
and going back a bit further…
Red Beans & Rice
Chilliwack
Lieutenant Pigeon
Mary’s Danish
Eve’s Plumb
Whitesnake
Whilst people happily eat Whitesnake and or the Flaming Lips, I don’t think they count as food 
Here is the eddited down list (no drinks, no misspellings, and no embedded food words, and everything available in some sort of normal store)
1910 Fruitgum Company
A Taste of Honey
Alice Donut
Ambrosia
Archers Of Loaf
Bass
Bass Hunter
Beans
Bees Make Honey
Better Than Toast
Black Eyed Peas
Black Grape
Black Stone Cherry
Blancmange
Blind Lemon Jefferson
Blind Melon
Blue Oyster Cult
Bowling for Soup
Bread
Buffalo Springfield
Buffalo Tom
Cake
Cake Like
Candy Skins
Caviar
Cherry Monroe
Cherry Poppin Daddies
Chicory Tip
Chocolate
Chocolate Watchband
Cibo Matto
Cinnamon
Close Lobsters
Coconuts Musume
Coldcut
Country Joe & the Fish
Cracker
Cream
Damien Rice
Don Cherry
Doug Clark and the Hot Nuts
Eagle Eye Cherry
Electric Prunes
Enter The Haggis
Fat Mattress
Fiona Apple
Fish
Flying Burrito Brothers
G Love and Special Sauce
Godley & Creme
Grant Lee Buffalo
Grapefruit
Gravy Train
Green Jello
Green Jelly
Gumbo
Half Man Half Biscuit
Hootie and the Blowfish
Hot Chip
Hot Chocolate
Hot Fudge
Hot Tuna
Humble Pie
Jawbreaker
Jello Biafra
Jelly
Jelly Roll Morton
Jellyfish
Jimmy’s Chicken Shack
Joseph Lamb
Junkfood
Ketchup
Kid Creole & the Coconuts
Lake Trout
Lamb
Lamb of God
Left Over Salmon
Lemon Jelly
Lieutenant Pigeon
Lightning Seed
Lisa Lisa and Cult Jam
Long Pigs
Lox and Vodka
Lubricated Goat
Marmalade
Martha and the Muffins
Mary’s Danish
Meat Beat Manifesto
Meat Puppets
Meatloaf
Menudo
Mighty Joe Plum
Moby Grape
Mustard Plug
Neneh Cherry
Neutral Milk Hotel
Nick Cave and the Bad Seeds
Octopus Project
Orange Juice
Papas Fritas
Peaches
Peaches & Herb
Peanut
Pearl Jam
Poi Dog Pondering
Poptart Monkeys
Prefab Sprout
Red Beans & Rice
Red Hot Chili Peppers
Red Red Meat
Reel Big Fish
Ribs & Brisket Revue
Richard Cheese
Sage Francis
Salt N’ Pepa
School Of Fish
Seafood
Sherbet
Smashing Pumpkins
Soup Dragons
Spearmint
Spice Girls
Squirrel Nut Zippers
Strawberry Alarm Clock
Strawbery Switchblade
String Cheese Incident
Sugar
Sugar Ray
Sugarloaf
Sweet Honey in the Rock
Taco
Tangerine Dream
T-Bone Burnett
The Apples In Stereo
The Banana Splits
The Cake
The Cookies
The Cranberries
The Eels
The Jam
The Jams
The Lemon Drops
The Lemon Pipers
The Lollipop Shoppe
The Magic Mushrooms
The Muffins
The Mutton Birds
The Partridge Family
The Peanut Butter Conspiracy
The Raspberries
The Sea & Cake
The Sea Urchins
The Seeds
The Spiders from Mars
The Sugarcubes
The Waterboys
The Watermelon Men
Thin Yoghurts
Tim Rice
Tommy Roe
Toni Basil
Ultimate Spinach
Vanilla Fudge
Vanilla Ice
Veruca Salt
Wild Cherry
Wings
A thread about bands with ‘food’ in the name, and no one mentions the excellent psychedelic, late '60s Capitol band Food? 
A few more off the top of my head:
Chicken Shack
The Candymen
The Tea Company
Mandrake Memorial
Buffalo
Strawberry Path
Flied Egg
You’re such a picky eater