It has a Roud Folk Song Index number of 16401.
In this version the names of the birds were Jack and Gill: These names seem to have been replaced with the apostles Peter and Paul in the 19th century.
[1] In American English, the variant "Two Little Blackbirds" is more common.
The adult, out of sight of the child, will mark in some conspicuous way the nail of the index finger of one hand and the nail of the second finger of the other hand.
Both hands are then shown to the child as fists (folded fingers downwards) with the two fingers with marked nails pointing forward – these represent Peter and Paul.