TAT-1 (Transatlantic No. 1) was the first transatlantic telephone cable system. Between 1955 and 1956, cable was laid between Gallanach Bay, near Oban, Scotland and Clarenville, Newfoundland and Labrador. It was inaugurated on September 25, 1956, initially carrying 36 telephone channels.
A description of the making of the valves used can be found here.
A submarine telephone cable between Great Britain and Ireland was in place in the 1940s.