Charles Babbage's Difference Engine #2 design of 1832, as constructed by the Science Museum, London, in 1991 for the bicentennary of B's birth.
(11/2004: A second copy was under construction for a US museum.)

Millionaire calculator.

Calculator.

A world war II 3-rotor Enigma machine. It is an electro-mechanical device not a computer, but it "inspired" the special-purpose code-breaking computers at Bletchley Park which decoded the Ultra intelligence for the allies.

SSEM c1949

[computer50] tells the story of the "Baby" stored-program computer, first run on 21 June 1948, and of other early Manchester computers.

The Harwell: "Britain's oldest original computer, the Harwell, is being sent to the National Museum of Computing at Bletchley where it is to be restored to working order. The computer, which was designed in 1949, first ran in 1951 and was designed to perform mathematical calculations; it lasted until 1973. ... The system was built and used by staff at the Atomic Energy Research Establishment in Harwell, Oxfordshire. ..." -- [BBC][3/9/2009].

U.S. Army Photo, #163-12-62, left to right: Patsy Simmers and ENIAC board, Mrs. Gail Taylor and EDVAC board, Mrs. Milly Beck and ORDVAC board, Mrs. Norma Stec and BRLESC 1 board, from Historic Computer Images by Mike Muuss.

recursion.

Meccano Babbage Difference Engine No 1
Designed by Tim Robinson of California
Built by Graham Jost
Model Engineers @ Monash U. 2008.