We are singing these (Tatton Singers summer concert). The second is Apple, apple, is about kissing the Miller's daughter. The third is The Old Woman And yes, the last one is faster than I can get the nonsense words out.
Julia was right about Bartok as well as Seiber I think. I've been googling, and I think Bartok collected the tunes, Seiber arranged them for choir in 1950 while living in England (he came here in 1935). A L Lloyd is credited with the words, but what I wanted to know and couldn't find out is. Did Bartok collect words with the tunes and is the nonsense 3rd song a translation, or Bert LLoyd's invention?

In the window, out the front door
Throw old nanny from the top floor
Pack her head into a basket
Let her sell it in the market
come on children welcome each one
At our party we'll have good fun
Drink and eat and roister allday
Farmer Johnny's bullock will pay