The predecessor of "ITR of N.Y." was the Bundy Clock Company founded in 1875 by Willard Bundy. He was in business as a clock maker and jeweller in Auburn, New York in 1885, and he designed and made a successful mechanical time recorder.
His brother Harlow organised the Bundy Manufacturing Company to produce these time recorders, and registered patents both in New York and London under the Bundy Clock Company, and the British Bundy Clock Company respectively in 1888.
In about 1900 the company moved to Endicott, New York, and became the "International Time Recording Company of New York".
In 1911, ITR merged with the Computing Scale Company of America and Herman Hollerith's Tabulating Machine Company to become the Computing-Tabulating- Recording Company (C-T-R).
In 1917, the new Canadian part of the operation was called International Business Machines Co.Ltd, and in 1924 C-T-R universally adopted this name. The IBM logo with the full name began to appear some time later.
In the UK things were a bit different.
The UK ancestry started with the British Bundy Clock Company, who were the UK arm of the Bundy Clock Company of New York State, and had registered patents in London in 1888. This UK company seems to have sold the parent company's products under license.
Before 1900, the UK arm had become the British Time Recording Co. (BTR), and was registered at 149, Farringdon Road, London, EC. BTR manufactured some of the USA product line in the UK, with products bearing the BTR logo and some aesthetic design changes.
In 1912 the company became incorporated in the UK and adopted the name used by the time recorder branch before the C-T-R merger in the US to become the International Time Recording Company Ltd.(ITR Ltd.).
Up to 1924 it appears that C-T-R's direct but limited trade in the UK was always through ITR Ltd. but a direct outlet in the UK became essential so in 1924/25 IBM joined ITR in the UK, and the two companies traded side by side under the same top management, sharing many services and facilities.
In about 1925 the firm of Howard Brothers, (which incorporated Dey Time Registers) of 75, Queen Victoria Street, London were absorbed into ITR Ltd.
When it became necessary for IBM to operate as a registered UK company, the senior company of the ITR and IBM partnership was chosen as the base on which to create IBM United Kingdom Co.Ltd. in 1951. This new company scooped up all the existing IBM operations in the UK.
Why the time recorder products never traded under the parent company name of C-T-R in the UK is open to conjecture, but ITR lived on in the UK right up to 1951 and operated as a wholly owned subsidiary of IBM from 1951-1962, during which time it was known as IBM UK Timer Systems Ltd.
In 1963 it reverted to the name of the International Time Recorder Company Ltd.
It later became "ITR International Time Ltd" and was taken over by Blick in 1982
Sources: IBM-UK history and Blick