This is a 1967 single by The Cocktail Cabinet and I haven't found any info on the artists, so here's a picture of a Cocktail Cabinet.
The single Puppet On A String on Page One records is some sort of a rarity and it even features as a collectable record in the Records Collectors Price guide at 15 pounds. (Although my copy is from 1995, I'm sure the record is worth 100's today)
The collectability of the record is because the b-side 'Breathalizer' is some sort of cult spaced out rare groove favorite and it's one of the rarer singles on the sought after Page One label. (The label that brought us the Troggs and Vanity Fare, whose Puppet will be featured later).
Breathalizer found it's way several compilations but Puppet On A String never did.
The Cocktail Cabinet
Puppet on a string b/w Breathalizer (Page One POF 046)
And as a bonus there's Reeves and Mortimer with their side splitting moment with Puppet on a string. It's from Shooting Stars, the TV show that was mainly bearable because it had Ulrika Johnson.
(listen at Youtube)