It's competition time for the most bodged radiator/hosepipe adaptor
The glue-free approach, but more components than Simon's so less reliable! For £1.09 on a
21.5-32mm adaptor from screwfix, some gash overflow pipe and hose tap thingy you could have this:
Admission

There's a bit of tape around the reducer which is sloppy in an old pipe
On a more serious note.... when flushing you want to avoid pushing crud through narrow (easily blocked) galleys in the engine. I figure the most likely place for this to collect is in the radiator and heater matrixes (should that be matrices?) so I would flush these individually in isolation. You will also need to take a rear heater hose off to get as much old coolant out of the system as a lot sits in the runs to the back and engine. (I had every hose off, the pump and thermostat and reckon there was still 1-2 litres (10%+ of full capacity)