Fabulous replies everyone, thanks.
More context: The Kirkburton registers mention Burnt Edge sporadically from 1677 to 1792. The 1841 census that you have found is the latest record. It is therefore not a one-off mishearing or misspelling of the name; even if it was just a single farm (quite likely), I am still surprised that it does not crop up more often given its long presence in the register.
Nearby locations of interest apart from Cartworth and Hepworth would include Holmfirth, Barnside, Maythorn, Foster Place, Flight Hill, New Mill... Penistone at a stretch (I have possible connections there but the distance is a little far from Holmfirth for me to be sure that they are the same people).
Possible locations gleaned from your replies and my research:
1) Birdsedge - it is a little far for me to be satisfied but it is interesting to note that there is not a single mention of Birdsedge in the Kirkburton registers I am using (despite mention of nearby hamlets), so it's possible it had a different name earlier. Still, there is no definite mention of a name change from Burnt Edge at any point in the 19th century.
2) Barnside - there is some mention of possible relatives living in Barnside and at a stretch I suppose there could be a name shift between the two. However, Barnside is given plenty of mention in the registers so this is unlikely.
3) Bedding Edge - if this was mentioned on the 1841 census alongside Burnt Edge then I find that pretty convincing myself! Very happy with this avenue of research but would appreciate any further input. The Abraham Beever in question is the direct ancestor I have been looking at and I had not come across his 1841 census record before, so thank you. No mention of Bedding Edge in the registers, so this is also promising (indicating a name change)
4) Brown Edge - semantically and phonetically related, so I am also intrigued by this option! Also no mention of it in the registers.
Also:
**Flooding a very good suggestion - the Holme Valley, especially Holmfirth has definitely been victim to several floods and I had not thought of the wider impact that flooding might have had
**Yes, agreed. The number of other 'Edges' in the area is bewildering and makes me wonder why this one didn't survive at least on one old map!
