The machine Ted Hoff was talking about was a Plessey System 250 (often written simply “P250” or “Plessey 250”).
A single–cabinet System 250 was delivered to Stanford University’s Digital Systems Laboratory in 1967 as a gift from Plessey and was still there when Hoff was doing graduate-student and post-doctoral work. In the oral-history interview he recorded for the Computer History Museum (CHM catalog number X5865.2010) he explains that

• the machine had “a couple of dozen fast registers that you did almost everything in”,
• main memory was quite slow so the CPU was designed to stay inside those registers as much as possible, and
• the whole processor occupied only a few printed-circuit boards that were quite separate from the memory frame.

That exposure convinced him, when Intel was asked in 1969 to build a set of special-purpose calculator chips for Busicom, that a complete general-purpose CPU could be reduced still further – to a handful of large-scale-integration chips or, ideally, to a single chip. That idea became the Intel 4004.

Why it qualifies as a “mini”.
Although the System 250 was used in air-defence and telephone-switching projects in Britain, it was physically small for its day: one 6-foot rack held the processor (constructed from a few dozen cards of ECL MSI logic), another rack held the ferrite-core store. In the late 1960s that size put it firmly in the “minicomputer” category, alongside machines such as the PDP-8 and DG Nova.

Quick specification (from R. M. Needham & D. H. D. Warren, “The System 250 – a capability computer” Proc. IFIP 68, and Stanford Electronics Research Laboratory Report SER-69-24):

• 24-bit word, 32 general-purpose registers (four banks of eight)
• 128 K-word magnetic-core main store (microcoded, capability-protected)
• Emitter-coupled-logic (ECL) implementation: 0.7 µs average instruction time
• One to two 19-inch cabinets for the whole system

It was the only machine of that size that Plessey themselves designed and built in that period, so when Hoff later referred to “a minicomputer donated by Plessey” the System 250 is the only candidate that fits both the donor and the description.

Primary sources

1. F. T. Hoff Jr., Oral history interview, Computer History Museum, 20 April 2010.
2. R. M. Needham & D. H. D. Warren, “The Plessey System 250 – A Capability Computer”, Proceedings IFIP 1968, vol. 2, pp. 544-548.
3. J. A. Gill, “Experience with the Plessey 250 at Stanford”, Stanford Electronics Research Lab Tech. Report SER-70-13, May 1970.

Secondary sources

• M. R. Williams & P. Campbell, “A Short History of British Minicomputers”, IEEE Annals of the History of Computing, vol. 16, no. 2, 1994, pp. 32-41.
• M. Ceruzzi, “A History of Modern Computing”, MIT Press, 1998, pp. 189-193 (discussion of Hoff and the 4004).