Burrgati was possibly an alternative name for Dhanggati E6, but the evidence suggests it was a regional variant of the Macleay Valley language (Wafer & Lissarrague's cover term for Dhanggati E6 Burrgati and Ngaku E4 2008:196).
Laves wrote 'burrgadi not much different from daŋati ─ like Ba:nbai-Kumb' (1929-32:1124), i.e. Baanbay E8 and Gumbaynggirr E7, which suggests a dialectal relationship between Burrgati and Dhanggati.
Holmer records a verb with a similar form and reference: ngaja ditjinj burugatinj 'I can talk Thangatti' E6; danguwa ngabajaru guwajitinj burugatinj 'my grandmother always spoke Thangatti' (1967:32).
Documentation on Dhanggati / Dunghutti E6 is relevant.
... spoken in the upper section of the Macleay River and extended to Armidale and Ben Lomond (Radcliffe-Brown 1929:400, in Wafer & Lissarrague 2008:196).
... at Wollomombi, which lies between Armidale and Ebor (Macpherson 1930:123, in Wafer & Lissarrague 2008:196).
... along the upper reaches of the Macleay and even further inland (Wafer & Lissarrague 2008:196).
... to the west and south of Bowraville (Morelli 2008:243).
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Ngaubu Bingayi Aboriginal Corporation / Dhanggati Language Group: https://dhanggati.org.au/
Dhanggati Language Group via Muurrbay ALCC https://muurrbay.org.au/
Speaker numbers were measured differently across the censuses and various other sources listed in AUSTLANG. You are encouraged to refer to the sources.
Speaker numbers for ‘NILS 2004’ and ‘2005 estimate’ come from 'Table F.3: Numbers of speakers of Australian Indigenous languages (various surveys)' in 'Appendix F NILS endangerment and absolute number results' in McConvell, Marmion and McNicol 2005, pages 198-230 (PDF, 2.5MB).