The Alan Price Set was the band Price formed after he left The Animals. This wasn’t their first hit – that was the Randy Newman song Simon Smith and the Amazing Dancing Bear* – but it was the first which Price wrote.

The Alan Price Set: The House That Jack Built

*Edited to add: I just remembered The Alan Price Set released I Put a Spell on You and Hi-Lili, Hi-Lo which were both hits before Simon Smith and the Amazing Dancing Bear.