There seems to be some confusion regards what is and what isn't the 'Nottingham Cast'. There is reference to it in J. W. Martin's books but I have also found a letter addressed to the editor of the Fishing Gazette dated 5th May 1905 that concisely explains it:
CASTING LIGHT FLOAT^TACKLE WITH A
NOTTINGHAM REEL.
Dear Sir, — Is it possible to throw an ordinary
light float tackle (say a small float and one small
shot) direct from a Nottingham reel ? I saw
accounts of long throws made with float tackle in an
account of a fishing tournament, and I wondered
how they were made. — Yours truly,
Nottingham Reel.
The lighter the weight the more difficulty there
is in casting direct from the Nottingham reel. Trent
experts can do wonderful things in this way, but
they have a method of starting the reel with the
fingers at the moment of making the cast, so that
great difficulty of starting the reel with a light
bait is overcome. Mr. Harry Spray does it to
perfection — in fact, I would give something to do
as he does, it must want a lot of practice. — Ed.
It would seem that it was similar to the Wallis Cast but without releasing the weight or float from hand. Starting the reel by hand may have involved batting the reel to start it as that method was often used to retrieve the float at the end of the swim or trot faster than when winding in.
It is also discussed in one of Cholmondley-Pennell's books where he professed to prefer the Thames Style cast that involves laying loops of line on the ground and retrieving the tackle by hand in the same way that fly-fishers do. Old Chumley's objections to the Nottingham style like so many of his observations showed that he had not actually fished that way.
There was also the Sheffield Style which involved long rods with small quill or dart type floats being cast like a fly line, back and forward until the desired distance had been achieved.
I don't know what the proper name for what I call the Loop Cast is. I remember that back in the 1960's when I first started fishing it was possible to order some float or match rods with extra rod rings on the lower section in order to facilitate this method. It was the first method I used only having a tiny and tinny centrepin reel and 9' cane and solid glass rod. Over the years I have used it for convenience but found that if I used more than two loops it often tangled around one or other of the rod rings.