In the 60s, there were 7 of them:
1960 - Tell Laura I Love Her / Ricky Valance
Welshman David Spencer paid tribute to the deceased Richie Valens with a similar stage name, and scored a chart-topper with a cover of Ray Peterson's U.S. hit. A UK BBC radio ban owing to the song's subject matter making it what they called a 'death disc', failed to prevent its success.
1962 - Nut Rocker / B. Bumble & the Stingers
U.S. Record producer Kim Fowley came up with a manic, piano-driven arrangement of a portion of Tchaikovsky's 'Nutcracker Suite' and captured the imagination of the British public at a time when instrumentals were particularly popular here.
1966 - Michelle/ The Overlanders
Covering a Beatles track in the mid-60s was virtually a guaranteed hit, and so it proved for U.K. group The Overlanders who started out as a folk group before deciding that the music of the Fab Four was worth a try. Wise decision!!
1968 - Fire / The Crazy World of Arthur Brown
UK artist Arthur Brown is mostly remembered for his zany semi-theatrical stage performances which included, when performing 'Fire', jumping around wearing a burning metal helmet!!!
1969 - In The Year 2525 / Zager & Evans
This record is the only one to have been a one hit wonder, using the British definition, in both the U.S. Billboard Hot 100 and the U.K. charts. It is also one of those few songs that have no chorus.
1969 - Sugar Sugar - The Archies
A fictional group in the Bubblegum genre, Ron Dante's lead vocals helped this infectious number stay at the top of the UK charts for a record-equalling 8 weeks.
1969 - Je T'aime Moi Non Plus / Serge Gainsborough & Jane Birkin
Another disc which was the subject of a complete BBC radio ban, this time for its sexual content. An instrumental written by Gainsborough, it had his girlfriend Birkin grunting and gasping in the background, leaving listeners in no doubt about what was supposed to be going on!! Once again, its progress to the chart summit was not impeded by the BBC's moralistic standpoint!
Strange that 3 of the 7 should be in the same year of the decade as it drew to a close. There seems to be no obvious reason other than pure coincidence.