Get some cheap, disposable dust sheets.
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Put them under and beyond the width of the radiator. Scrunch up some old towels/tea towels and put them on top of the dust sheet, then pour hot soapy water over and through the radiator.
Dry the outside and underneath straight away.
The dust sheets and towels will be dripping, so have a bowl or bucket handy to stuff them in.
Go back 2 or 3 times to wipe the drips that have accumulated at the bottom of the radiator.
I do this about 4 times a year, and in between, just wipe the outside of the radiator with a damp cloth