Ann Davies played Jenny in the The Dalek Invasion of Earth.
In the documentary Future Memories, Davies claimed that Jenny was under consideration as a replacement companion following the departure of Susan Foreman at the end of the episode. Davies also noted that she became friends and neighbours with actress Jacqueline Hill. This recollection incorrectly suggested that perhaps Davies was, like Pauline Collins, a "companion-that-almost-was".
However, it was only Jenny that was considered as a replacement, not Davies herself. The extensive notes left behind of this period of Doctor Who's history clearly indicate that the character was originally called "Saida" and had been offered first to Pamela Franklin on about 17 August 1964. Lambert had made this offer because BBC1 Controller Donald Baverstock had agreed to renew Doctor Who for thirteen weeks beyond the end of Carole Ann Ford's contract, which lasted until the conclusion of Dalek Invasion.
Almost as soon as he had agreed to the extension, however, Baverstock withdrew the offer as a ploy in the renegotiation of William Hartnell, Hill and William Russell's contracts. In the waning days of August, 1964, Verity Lambert was forced to consider that the whole show might end at the conclusion of the present production block. Indeed, Baverstock flatly told her on 19 August 1964 that "it would be unwise to establish the new girl as a permanent member of the cast in the last episode" of Dalek Invasion and even suggested that if the salary negotiations failed, "a totally new or partly new group of principals" might have to be considered. Lambert therefore reversed herself and ordered Jenny be written as a one-shot guest. The deal with Franklin fell through and the now-smaller role was subsequently offered to Davies.
It therefore seems extremely unlikely that she would have ever believed herself actually in the running for a regular part on the programme, because by the time the part was actually offered her it was firmly that of a secondary guest character.
She was married to Richard Briers from 1956 until his death in 2013.
Biography from the TARDIS Data Core article, licensed under CC-BY-SA