Here are some transcriptions and links to holding relating to the development of museum anthropology at Oxford in other archives set in chronological order:

General:

Notice by the Board of Studies for the Natural Science School of the University of Oxford ... Oxford 1872

1872 article in Nature vol vi pp. 57-58 regarding 'The Oxford Scheme of Natural Science'

The Times (London) 23 May 1877 University Intelligence (University of Oxford plans regarding museums)

University Gazette references to Pitt Rivers Museum 1883-1920: Part 1 1883-1899; Part 2 1899-1910; Part 3 1910-1920

Anthropology by Tylor (1881, first edition)

Letter to Tylor from J.O. Westwood regarding anthropological lectures 1882

Anthropology by Tylor (1889, second revised edition)

Oxfordshire press accounts of the Museum 1887-1891

Correspondence between William Flinders Petrie and Henry Balfour regarding Balfour's possible move from Oxford in 1891 [held by Petrie Museum, University College London]

Miscellaneous notes on some of Tylor's papers and lectures

Relevant manuscripts etc accessible via the Spencer and Gillen website

Henry Balfour's Presidential Address to the Royal Anthropological Institute, 'The relationship of museums to the study of Anthropology' 1904'

Andrew Lang's essay, 'Edward Burnett Tylor' from Anthropological Essays ... [1907]

Vernon's description of the Pitt Rivers Museum [1909]

'Anthropology' R.R. Marett 1925 [6th edition]

Henry Balfour's Frazer Address 1939, 'Spinners and Weavers in Anthropological Research'

R.R. Marett's account of anthropology at Oxford taken from A Jerseyman at Oxford (1941)

Extracts from T.K. Penniman's A Hundred Years of Anthropology (1965/ 1974)

Rolleston's 'On the 3 periods known as the Iron, the Bronze and the Stone Ages' [1878]

Augustus Pitt-Rivers related material

See here for transcribed primary documents relating to the founding collection at the Pitt Rivers Museum

See here for the scans of all the Pitt-Rivers correspondence held at Salisbury and South Wiltshire Museum [NB this resource is not yet complete]

Transcriptions of some of Pitt-Rivers' lectures and papers, including drafts, which are of relevance, some from Salisbury and South Wiltshire Museum's Pitt-Rivers papers

See here for a list of all available transcriptions of Pitt-Rivers unpublished letters and papers

Tylor related material:

Natural History Museum

Archives - L MSS TYL: Notebook relating to EBT’s life by Lady Tylor. The entries are brief, stating where EBT was and when, and sometimes for what purpose. Illnesses and deaths of people close to the Tylors are also noted. Most of the entries refer to the places that the Tylors travelled to each year, and how long they stayed there.

British Library

Add MS 5024 - correspondence 1859-1906 (97 items)

Letter to Tylor from J.O. Westwood regarding anthropological lectures 1882

UCL

Galton Papers - NRA 19968 Galton. Letters to Sir Francis Galton

MS ADD 88 - NRA 14256. Correspondence with G. C. Robertson

Salisbury and South Wiltshire Museum

Letters to Augustus Henry Lane Fox Pitt Rivers

American Philosophical Society

Correspondence with Franz Boas in Boas-Rukeyser Collection, 1869-1940. B/B61.ru

National Anthropological Archives - Smithsonian

Andrew Lang's essay, 'Edward Burnett Tylor' from Anthropological Essays ... [1907] 

Rolleston related material

Apart from the Ashmolean Museum manuscript collection holdings for Rolleston, listed under Primary Resources / Ashmolean, there is other Rolleston correspondence held at the Wellcome Library, see here for a catalogue.