Sadly a lot of TOTP performances from the 1960s have been lost, but check out this fairly extensive list of TOTP performances from the 1960s that exist in the archive.
Dave Clark Five performing 'Bits And Pieces'
The Rolling Stones performing 'Not Fade Away'
The Hollies performing 'Just One Look'
Gene Pitney performing 'That Girl Belongs To Yesterday'
The Supremes performing 'Baby Love'
Roy Orbison performing 'Oh Pretty Woman'
The Moody Blues performing 'Go Now'
The Byrds performing 'All I Really Want To Do'
Jonathan King performing 'Everyone's Gone To The Moon'
Sonny & Cher performing 'I Got You Babe'
The Shadows performing 'Don't Make My Baby Blue'
Herman's Hermits performing 'Just A Little Bit Better'
Procol Harum performing 'A Whiter Shade Of Pale'
The Beatles performing 'All You Need Is Love'
Pink Floyd performing 'See Emily Play'
Tom Jones performing 'I'll Never Fall In Love Again'
Alan Price Set performing 'The House That Jack Built'
Dave Davies performing 'Death Of A Clown'
The Turtles performing 'She'd Rather Be With Me'
Cliff Richard performing 'All My Love'
Diana Ross & The Supremes performing 'Reflections'
Lulu performing 'Love Loves To Love Love'
Dave Dee, Dozy, Beaky, Mick & Tich performing 'Zabadak!'
Long John Baldry performing 'Let The Heartaches Begin'
The Rolling Stones performing 'Let's Spend The Night Together'
Engelbert Humperdinck performing 'The Last Waltz'
The Bee Gees performing 'Massachusetts'
Manfred Mann performing 'Mighty Quinn'
Amen Corner performing 'Bend Me, Shape Me'
Dave Dee, Dozy, Beaky, Mick & Tich performing 'Legend Of Xanadu'
Herman's Hermits performing 'I Can Take Or Leave Your Loving'
The Move performing 'Fire Brigade'
Brenton Wood performing 'Gimme Little Sign'
Alan Price Set performing 'Don't Stop The Carnival'
Status Quo performing 'Pictures Of Matchstick Men'
The Foundations performing 'Back On My Feet Again'
Cilla Black performing 'Where Is Tomorrow'
Manfred Mann performing 'My Name Is Jack'
Julie Driscoll, Brian Auger & The Trinity performing 'This Wheel's On Fire'
Don Partridge performing 'Blue Eyes'
The Hollies performing 'Sorry Suzanne'
Donald Peers performing 'Please Don't Go'
Marvin Gaye performing 'I Heard It Through The Grapevine'
Sandie Shaw performing 'Monsieur Dupont'
Cliff Richard performing 'Good Times (better Times)'
Peter Sarstedt performing 'Where Do You Go To (my Lovely)'
Cilla Black performing 'Surround Yourself With Sorrow'
The Bee Gees performing 'The First Of May'
The Tymes performing 'People'
Lulu performing 'Boom Bang-a-bang'
Love Affair performing 'One Road'
Stevie Wonder performing 'I Don't Know Why (i Love You)'
Dave Dee, Dozy, Beaky, Mick & Tich performing 'Don Juan'
Marmalade performing 'Ob-la-di-ob-la-da'
Clodagh Rodgers performing 'Goodnight Midnight'
Scaffold performing 'Lily The Pink'
The Rolling Stones performing 'Honky Tonk Women'