Babar
BBC
1968? 01/1989-06/1991 (US)
Animation

Bad Boyes
BBC
September 1987 - December 1988

Baggy Pants and the Nitwits
September 1977 - October 1978

Bagpuss  
BBC
12 February 1974 - 07 May 1974
Animation

Bailey's Comets
1970s

Balamory  
BBC
2000's
Story

Banana Splits
ITV
1968

Bananaman  
BBC
03 October 1983 - 15 April 1986
Animation

Bananas in Pajamas
1990s

Bangers and Mash
1988

Barbapapa
BBC
1970 - 1973 / 1976?

Barnaby
BBC
04 April 1973 -

Barney and Friends
Five
Pre-School

Barriers
ITV
1983

Basic Maths
ITV
1981 - 1984

Basil Brush Show
BBC
1968
Puppets

Batfink
1960 - 1980s

Batman [Cartoon]
Animation

Batman [Live Action]
ITV
1966 - 1975
Live Action

Battle of the Planets
1970s

Batty Adventures
BBC
24 September 1987 -

Beachcomber Bay  
Five
06 September 1999 - Unknown
Puppets
Transmitted as part of Milkshake

Beachcombers
ITV
1972 - 1984

Bear Behaving Badly  
CBBC

Bear Behind, A  
BBC
17 October 1988 -

Beat the Border
ITV
1964
Music

Beat the Teacher
BBC
1984 - 1988
Game Show

Behind the Bike Sheds
ITV
1983

Bellamy's Backyard Safari
BBC
1981
Factual

Bellamy's Bugle
ITV
1986

Belle and Sebastian (aka Belle et Sébastien)
BBC
October 1967 - January 1968
Live Action

Benji, Zax and the Alien Prince
1984

Bertha  
BBC
01 April 1985 - 18 June 1986
Animation
Transmitted as part of See-Saw

Big Bag
ITV
1998

Big John, Little John  
BBC

Bill and Ben
BBC
2001
see also Flower Pot Men

Billy Bunter

Birdman
ITV
1980s

Biskitts
1970s

Bitsa
BBC
Art

Bizzy Lizzy  
BBC
04 April 1967 -
Transmitted as part of Watch with Mother

Blackness, The    
ITV
17 January 1961 - 21 February 1961
Live Action

Blue Peter
BBC
October 1958 - Present
Magazine

Bluffers, The (aka De Bluffers)  
Channel 4
07 January 1990 - 01 April 1990
Animation

BMX Bandits
1984

Bob the Builder
BBC
1999

Bod  
BBC
23 December 1975 - 16 March 1976
Animation

Bodger and Badger
BBC

Bonny
BBC
1974

Book Game, The
BBC
1982

Book Tower, The
ITV
1979 - 1989

Borrowers, The
BBC

Boss Cat (aka Top Cat)
BBC
1973?

Brainchild
BBC
1974 - 1975

Bravestar

Break Point
BBC
1985

Brendon Chase
ITV
1980ish
Drama

Bric-a-Brac  
BBC
01 October 1980 - 17 December 1980
Story
Transmitted as part of See-Saw

Brolly's, The  
BBC
13 September 1990 -

Brum
ITV
Animation

Bubblies
ITV
1980s

Bucky O'Hare

Budgie the Little Helicopter  
ITV

Bugs Bunny

Bumblies, The  
BBC
14 February 1954 - 12 December 1954
Puppets

But First This  
BBC
Programming

Button Moon  
ITV
08 December 1980 - 01 December 1988
Puppets

Butt-Ugly Martians, The

Byker Grove
BBC
1989 -
Drama