The development of magnetic tape recording is generally credited to German scientists. It is their Magnetophone that provided the inspiration for the Ampex recorder, which was the first truly high-fidelity tape machine. From Wikipedia:
Early magnetic tape recorders were created by replacing the steel wire of a wire recorder with a thin steel tape. The first of these modified wire recorders was the Blattnerphone, created in 1929 or 1930 by the Ludwig Blattner Picture Corporation. The first practical tape recorder from AEG was the Magnetophon K1, demonstrated in Germany in 1935.
Although lesser-known, the British Broadcast industry had a similar machine in use in that same decade. The following account is given in the May 1954 issue of “Audio.”