In the late 1920s the British were seeking a replacement for their book cypher systems, so two commercial Enigmas were purchased for evaluation. In 1935 the government commissioned Creed & Company to manufacture 'Enigma type' machines. By 1936 Creed had made its first devices, which became known as the RAF Enigma with Type X attachments, and subsequently as Typex.
Typex was a five rotor machine, as opposed to three or four in the Enigma. This change alone adds no security, because a rotor only turns after enough keypresses have occurred to turn all the rotors to the left of it. In the case of a three rotor machine that would require 26 x 26 = 676 keypresses before the third rotor would have any effect. In the case of a four rotor machine the message would have to be 676 x 26 = 17576 letters long – and messages this long simply aren't sent.
In fact the first two rotors didn't even bother being geared, for simplicity. However, these additional slots meant that the number of different ways rotors could be inserted into the machine increased greatly. In a classic Engima machine with (say) ten rotors, you can have 103 = 1,000 different ways to arrange them, but in the Typex there were 105 = 100,000 possible combinations.
When faced with the task of decoding Enigma type messages, the British built many "reverse-Enigma" machines (the bombes), each with one possible selection of rotors during a run. With so many more possibilities, the Germans would find this sort of attack against the Typex impossible.
Another improvement the Typex had over the Engima was that each rotor in the machine contained several notches that would turn the "next rotor". Whereas the Enigma would turn after every 26th key press, the Typex might change after 5, 11, 13, and 21 keypresses. This change helps eliminate the number of potential patterns that could be found.
But by far the greatest change was to simply use Typex as little as possible. Whereas the Germans routinely encrypted almost all of their messages in their various networks using Enigma, only the British Army high command and the RAF, used the Typex regularly. Other branches still performed all of their encryption by hand using older book-based methods. The supply of the Typex machines was kept severely limited, and no field units were ever allowed to have machines.
From 1943 the Americans and the British signed the Holden Agreement and BRUSA to develop a Combined Cipher Machine (CCM). The American SIGABA (M-134-C) was similar to Typex in concept, although the Americans never allowed the British to see it, so attachments were built for both that allowed them to read messages created on the other.
It is believed that the CCM was never broken by the Axis. Although a British test cryptanalytic attack made considerable progress, the results were far worse than against the Enigma, due to the increased complexity of the system and the low levels of traffic. A Typex machine was capture by German forces, but it was without rotors. Their inability to use the machine in order to crack Typex messages may have convinced them even more of the security of Engima.
Typex machines continued in use after the war up until the 1970s (the New Zealand government disposed of its last machine in 1973). This was one of the reasons the British kept the Ultra secret for so long; another was that they continued to read the traffic from other nations using Enigma and Typex, while their users continued to consider them secure.