This repair is the kind of thing Sugru excels at. Regular glue would be useless, & hot glue wouldn't stick. Epoxy would be rock hard, so you couldn't get the retaining lug through the hole once set, & doing it 'wet' would likely ruin it as it would glue the rotating part to the fixed part of the cleaner. Plus you'd have to fully strip the sweeper to get access to the blind side of the hole.
Sugru sets more like a silicone rubber, so has the essential 'give' that makes this repair almost trivial!
Step 1: Find the Brush
Now grab your sugru!
Ours was provided free by Sugru, who sent us about ten free packs to see what we could come up with. You can get a selection pack from B&Q though.
Step 2: Add Some Magic. Er, Sugru.
Mould it roughly into a square that matches the remaining half.
Now carefully push it a little into the hole so you can get the size exact. Scrape down the sides so that it is a good fit, then add a little more at the top to match the retaining bulge.
Once happy, leave it to cure overnight.
Step 3: Replace the Brush
You can see the brush in the second photo, spinning as it should. :-)