Google Maps suggested that you can cycle along either bank of the canal. Actually the south bank is only suitable for walkers: very narrow paths, uneven terrain, steep flights of steps, cross-country in places!
The Greenway on the north side, however, is completely flat, wide, and suitable for any kind of bike (I was on a Brompton). You can just go there and back, or go there, nearly to the end, and then look around via villages to get back to Stratford, although the signage could be better (I took a wrong turning at least once).
Near the town is a place you can hire bikes, and a railway carriage converted into a tea-room, serving tea, coffee, cakes, ice-cream, etc.
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