A good post Normandie18. I'm ex Glosters and so have an interest in all cloth insignia worn by my old Regiment. I have seen several embroidered "genuine" 56th Ind Inf Brigade on eBay, which look very homemade to me, and recently a "genuine" printed version for sale by a dealer.
All the evidence that I have points to only the full size badge being worn by my regiment whilst the were part of the Independent Infantry Brigade, and the cut down version being worn once they ceased to be Independent and came under the command of the 49th Div. I have no evidence that my Regiment ever wore the circular version you illustrate.
I hope the above, from a Gloucestershire Regiment perspective may be useful?
Regards,
Ken