In America, Singer produced a folding iron to go into the case along with the machine. I have never seen one of these irons for sale in the UK, I am a frequent user of Ebay and have seen the USA ones fairly regularly.
My sister went into a local Vintage Shop in Yorkshire and found two vintage folding travel irons. They are not a Singer brand but very similar. She kindly gave one to me, as you can see, its hardly been used at all.
It comes in a neat well made case. Haven't tried to see if it will fit in the 221K case, I suspect it might be a bit of a squeeze.
It very comfortable to use and its got some weight about it so lovely to iron with.
Full instructions included. Not sure that I will be plugging it into a UK light fitting, will use an adaptor.
This is what I normally use next to my Sewing Machine.
Was using the 201K today as I needed to sew some leather. The iron goes really well with it, much better than plastic!