Strachey left the National Research Development Corporation in 1959 and set up formally as a private consultant in June 1959, with Peter Landin as his assistant (see MS. Eng. misc. b. 251/A.44-MS. Eng. misc. b. 252/A.60). While maintaining relations with official work through the National Research Development Corporation and other committees, etc., he undertook commissions from computer manufacturers on the design and use of computers. Much of the material in the folders below should therefore be read in conjunction with the relevant folders in the consultancies series. Consultancies, to which cross-references are given where possible.

From about 1960 Strachey adopted the (not invariable) practice of date-stamping his notes, and these dates are given in the items below, as well as the titles or descriptions on the original folders. In the case of loose papers, however, it has not always been possible to assign them with certainty to a specific project among the several in which Strachey was often simultaneously involved at this period.

His work on LISP for the EMIDEC 2400 (see MS. Eng. misc. b. 266/C.121-MS. Eng. misc. b. 267/C.135, MS. Eng. misc. b. 278/D.14-MS. Eng. misc. b. 279/D.32) consolidated his approach to the mathematics and semantics of high-level programming languages, and led to his participation in the work of the Cambridge group on CPL (see MS. Eng. misc. b. 268/C.136-MS. Eng. misc. b. 272/C.184) and his Fellowship at Churchill College (see MS. Eng. misc. b. 253/A.61). His private consultancy business was formally wound up in 1964 before his visit to M.I.T. and his appointment at Oxford.