I listened to this LP about 2000 times during the first years of my life. Since I worked the record player myself; it was soon covered in scratches and jumps - but never became unplayable. Whyton was a skiffle star of the 1950s, and in my early years he was a continuity announcer on the local Devon TV channel (Westward) - along with a cat glove pupper called Willum.
Certainly these are good performances, albeit in an American folk style. Note the sped-up mouse-voice songs - which could be played at 16 rpm to reveal Wally Whyton's normal voice.
When my kids were young, we had an excellent video of English folk style nursery rhymes - here is a sample:
Yes, that's (the great) Martin Carthy doing Over the Hills. And (the great) Shirley Collins...