The telegraph arrived in Newmarket surprisingly from Norwich, not as I would have expected from London. It was provided by the The Electric Telegraph Company that was merged with the International Telegraph Company in 1853 to become The Electric & International Telegraph Co. They had already provided signalling systems for the railways in East Anglia before entering into road line construction. The all powerful Jockey Club were not going to have poles and wires in the town, not from an aesthetic point of view, but because all these overhead wires carrying electricity might frighten the racehorses.

15th January 1859 From the Newmarket Journal: The posts for the telegraph from Norwich to London have been erected as far as Newmarket for several weeks past, but some difficulty appears to have arisen in passing the town, as strong objections were made by the Jockey Club to the placing of the posts. This was doubtless a source of considerable inconvenience to the company.
It seems that eventually the Jockey Club, finding that they were not going to prevent the telegraph coming into the town agreed to underground cable. This must have been an incredible extra expense to the Company.
5th March 1859: Newmarket Electric Telegraph. It was decided that the wires of the telegraph from Norwich to London are to be carried through the town in pipes under the main street, for some considerable distance upon the London and Bury turnpikes, and about sixty labourers were employed in making the tunnel for that purpose. Several of the posts have been removed from the east entrance of the town as far as the exercising heath extends, in consequence of the noise from the wires etc. being objected to by owners and trainers of race horses.
1888 From the Newmarket Journal: Negotiations have been going on with the South of England Telephone Company for the establishment of a branch at Newmarket. We now understand that the Company have decided to open an office here, and have hired one of Mr Golding's houses adjoining Mr Glenister’s new shop, in the High Street, for the purpose. The construction and apparatus will accommodate 60 clients; it is to be hoped their enterprise will meet deserved success.
Mr Golding bought up most of the property between the Rutland Arms and the Star Inn in the High Street that once belonged to the Crown and was part of the old royal palace; this included Palace House that is now the tourist information office. In Kellys Directory, John Glenister was listed as a tailor, hosier & outfitter (formerly of Poole’s Savile Row, London) High Street and Market Street.
It is now 1888 and it seems that the telephone exchange proposed in 1886 has still not arrived in the town. Although two of the residents, Mr William Benjamin Shepherd, grocer etc, & agent for W & A Gilbey, wine and spirit merchants, High Street. ( 1896 Kellys) and James Ryan, trainer, Green Lodge, The Severals (1896 Kellys) have had what was termed a ‘Private Wire’ or intercom installed between their respective houses and business premises.
As a result of the argument with the Jockey Club the first telephone exchange was not set up in the town until around 1898, the line coming from Norwich.
While the National Telephone Company were installing their exchange, the General Post Office opened an exchange in 1898, probably in the Post Office in High Street.
Post Office Telephone Exchanges Newmarket
7th July 1898 opened
31st December 1899 2 Subscribers
31st December 1900 3 subscribers
31st December 1904 4 Subscribers

In 1908 the National Telephone Company exchange was situated in Kingston Passage (adjacent to York Buildings once occupied by Mr Bullman’s drapery emporium) where they rented a holding for £35 a year. It is likely that it was the same premises which the NTC had started in 1897/8, as it would have been impracticable to move all the overhead wires to new premises except in the most extreme circumstances. The expiry date of the lease was in line with the eventual Post Office buy-out of the National Company which took place in the same year, 1912.
From the Newmarket Journal 30th December 1911: Newmarket is now in telephonic communication with Paris. Calls may be made from the Post Office the charge being eight shillings for three minutes. (The Paris service had opened on 1st April 1891)
In 1923 the exchange moved to new GPO premises in the High Street. .

From 1923 the Post Office and telephone exchange was sited
in the High Street on the corner of New Cut

A 1920s picture of High Street showing the new Post Office, 4th building from the left.
It would have been unbelievable at the time that it would be reduced to rubble by 1941, as a picture on the following page shows

Telegraph poles and numerous overhead wires carried communications in and out of Newmarket, here seen bordering Cambridge Road
All the three photos above from the Roger Newman collection,

The electric telegraph history researched by former NLHS committee member David Occomore for his book 'News from Newmarket'