Until very recently it was believed that Jack and Jill, the two windmills at Clayton in West Sussex, most probably got their names from trippers travelling by train from London to Brighton in the late 1920s, as the earliest written (and dateable) reference to the mills having these names was 1925.

This has now been superceded by "Gill" handwritten on the reverse of a postcard taken from a 1914 photo.    That date has been independently confirmed by reference to a series of letters written in 1915, one of which refers to "Gill" and to the postcard.

Jack and Jill went up the hill
to fetch a pail of water
Jack fell down and broke his crown
and Jill came tumbling after.

The original nursery rhyme has fifteen verses, here are the next three : -

Up Jack got and home did trot as far as he could caper and went to bed to mend his head with vinegar and brown paper.

Then Jill came in and she did grin to see Jack's paper plaster. Her mother whipped her across her knee for laughing at Jack's disaster.

Now Jack did laugh and Jill did cry but her tears did soon abate then Jill did say that they should play at see-saw across the gate.

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Apparently, Scandinavian mythology has it that one evening two children, Hjuki and Bil, were walking home with a pail of water when Mani, the Moon Man, came down and carried them off to the Moon.    In Sweden the Moon spots are said to resemble the two children with a pail slung on a pole between them.

Hjuki derives from the verb "Jakka", to increase or assemble whilst Bil derives from "Bila", to break up or dissolve, thus linking them to the Moon's cycles.

Shakespeare tells us that the Moon is "Governess of all the floods" hence the pail of water.

It is fairly easy to derive Jack from (H)juki and Jill gives a natural alliteration whilst providing a feminine interest.

A vinegar and brown paper plaster is a genuine old folk remedy for cuts and scrapes.

Dewponds apart, there is no easy explanation for water being placed at the top of a hill.     Castles, strategically placed on hill tops, had deep wells, but that seems unlikely.    One possible answer could be that water located 'up the hill', such as springs, would be free from the water-borne diseases that were common in towns and villages during the Middle Ages.
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Another suggested origin for the nursery rhyme is 18th century France; with King Louis XVI [Jack] being beheaded (literally losing his 'crown') along with Marie Antionette [Jill].
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It is thought that Kilmersdon's Jack and Jill, were a 16th century couple who climbed every day to a well at the top of the hill in this Somerset village.