The oldest surviving canon in English is Sumer Is Icumen In, which is for 4 voices, plus 2 bass voices singing a ground (that is a never changing repeating part). The first published rounds in English were printed by Thomas Ravenscroft in 1609; Three Blind Mice appears in this collection, although in a somewhat different form from today's children's round.
Three Blinde Mice,
three Blinde Mice,
The Miller and his merry olde Wife,
shee scrapte her tripe licke thou the knife.
Many of the rounds printed by Ravenscroft also appear in a 1580 manuscript (KC 1), and several are mentioned in Shakespeare's plays, so these little ditties seem to have been quite popular.
For further reading: