There's a bit of a misunderstanding in the question, as wireless telegraphy is an archaic term for radio communications. A ship with a wireless telegraph by definition had a radio.

The Royal Navy was an early adopter of the radio, with the first experiments being done in 1895. The first champion of the radio in the RN was Henry Jackson, commander of the RN's torpedo school, based at HMS Defiance in Devonport. Jackson's father-in-law was a mathematician, Samuel Burbury, who had published several papers on electromagnetism. Through discussions with Burbury, Jackson had, before Marconi's invention, been considering the use of radio waves for ship identification and tactical control. In 1895, following his assumption of Defiance's command, Jackson began serious work on radio communication, constructing a transmitter and receiver. By August 1896, he had a system that could be used to transmit systems from one end of Defiance to the other. On the 31st August, he would meet Marconi at a conference on radio held by the War Office. This was the start of a lasting friendship, and long-term professional relationship. Jackson saw rapid improvements, and by the end of 1896, had placed a radio system aboard one of Defiance's tenders. In 1897, Jackson's radio was placed aboard the torpedo boat HMS Scourge, another of Defiance's tenders. This system was capable of transmitting messages between Scourge and Defiance over relatively large distances - up to five miles. This was the first example of ship-to-ship communication. In October, Jackson set up a radio link between Defiance and the Port Admiral's house in Devonport. However, he would have to take a break from his radio work as he became Naval Attache in Paris from the 1st November. He would resume his work in 1899, on the RN's summer manoeuvres. During these, three ships were equipped with radio systems, including HMS Juno, under Jackson's command (the two others were Europa and Alexandra). These manoeuvres confirmed the utility of radio, and the RN soon moved to take action on this.

Soon after, tensions in South Africa resulted in the start of the 2nd Boer War. Shortly after the beginning of the war, Marconi convinced the War Office that radio would be useful for ship-to-shore communications, especially in the troop-ship choked harbours of Durban and Cape Town. Five radio sets were hired and sent south. Arriving on the 24th November 1899, the operators found that the plan had changed. Instead of remaining in port to communicate between ships and shore stations, they were to be sent into the field. Radio sets were deployed at the towns of Orange River, Belmont and Modder River, with a further set deployed forward to Enslin to provide advance warning of a Boer attack and a main station at the railhead of De Aar. However, these systems worked poorly. The thunderstorms prevalent in the South African summer caused serious interference. The systems, designed for shipboard use, didn't have long masts for the antennae, while improvised solutions such as bamboo poles or kites proved to be unsuitable for the arid South African climate. Additionally, the soil conductivity was poor, reducing the effectiveness. In February 1900, Marconi, defending his system, criticised the British Army for their failure to make sufficient preparations, not without justification. In an act of petty revenge, the Director of Army Telegraphs ordered the radio telegraphs to be dismantled and removed from service. The Army's loss was the RN's gain. The systems were requisitioned for the use of the squadron blockading Delagoa Bay. By March, they had been fit to five cruisers, Thetis, Dwarf, Forte, Magicienne and Raccoon. Here, they proved their use, allowing the ships to operate out of visual range of each other, greatly extending the reach and effectiveness of the blockade. By retaining one ship in Delagoa Bay, within range of a shore station with a telegraph, speedy communication could be made between the squadron and the naval HQ at Simon's Town, some 1600 miles away. This experience, combined with the successful manoeuvres of 1899 (and a repeat performance in the 1900 manoeuvres), convinced the RN that radio was needed. By the end of 1900, 42 ships and 8 shore stations were equipped with radio equipment, using a combination of Marconi and Jackson systems. The RN would continue to fit radio systems to its ships, and in 1904, a wireless telegraphy school was established aboard HMS Warrior. In 1907, the decision was made to fit radio to destroyers, as well as to the main fleet units that had previously been receiving the systems. By 1909, shore stations had been set up covering all of Britain's home waters, as well as the waters around Gibraltar and Malta.

However, during WWI, radio was just one part of the RN's signalling arsenal. Flag signals, semaphore, and Morse signal lights were equally important, if not more for tactical use. There were two main reasons for this, both relating to the systems used. These early radios were 'spark gap' transmitters. These used a spark generated between two cables to create the radio signal. This was a noisy signal, creating a lot of radio interference, even on distant frequencies. This effectively meant that only one ship could transmit at any one time. Secondly, the system was very vulnerable to damage. Any short circuit in the system would prevent the spark travelling through the antenna. To prevent these forming, the systems were heavily insulated. However, any cut to the insulation would cause short circuits, and disable the radio system. In battle with shell splinters flying everywhere, the system proved unreliable. The development of the 'continuous wave' radio system, which relied on vacuum tubes, would make radio truly effective for naval use. While such systems were available during WWI, they were in their infancy, and were considered to be too fragile and unreliable for use.

Sources:

Wireless Telegraphy During the Anglo-Boer War of 1899-1902, Duncan C Baker, Military History Journal, Vol 11 No 2, 1998

Captain Henry Jackson of HMS Defiance: Victorian Ship-to-Shore Communications Pioneer, John Hooper, PDS Print, 2007

Fighting the Great War at Sea: Strategy, Tactics and Technology, Norman Friedman, Seaforth, 2014