Katy Manning, who played Jo Grant [from 1971 to 1973], was leaving, and so Barry [Letts, the producer] had been quietly auditioning for a new companion. Eventually they thought they'd found the right girl, so they signed her up and began rehearsals. I can't tell you who she was; I don't think that would be fair. But I can say she didn't get on with Jon [Pertwee]. It just didn't work between them apparently.This gives several more details than the hitherto received wisdom, which was simply that a different companion played by a different actress had been proposed but that the production team had not gone ahead with her. Now Elisabeth Sladen adds that i) the chemistry did not work between Ms X and Pertwee; ii) Ms X was well-endowed; iii) Ms X was not short enough (Katy Manning is 5'0" = 153 cm, Sladen was 5'4" = 162 cm.) So who was Ms X?
...and that was the problem with this girl. Evidently she was quite big, by which I mean, very busty. If you're spending half a show running along dark tunnels, that's going to pose one or two problems. More importantly, I don't think it's unfair to say that the Third Doctor's character is exactly the sort who thrives on being surrounded by smaller women. Jon loved Katy because she's mad as a hatter, warm and funny, but crucially, she's little. And I think Jon was the same as his Doctor in that respect; his personality, his very being, responded differently to having smaller girls around him. So it didn't work out with Katy's replacement. They paid her off, and started again.
Andrew Pixley has been through the BBC's archives, and reports:
There's nothing about this in the production file on The Time Warrior - although other actors in the Pertwee era who were contracted and not used have their paperwork present in the files... Who else could be likely candidates without going through every actress personnel file in 1973? How about Susan Jameson, whom Barry Letts has mentioned often in interviews about wanting to cast? Nope. Or maybe Fiona Gaunt, who then turns up in Moonbase 3 which was made about the same time? Nope... would there in fact even be a contract issued for this unknown actress if regulars were contracted so close to (if not after) their start date?I must say that just from my own experience it has been the exception rather than the rule that I turn up to work on my first day at a new job with the physical paper contract already signed. (Perhaps I am not careful enough.) So there may have been some word-of-honour understanding rather than a legal document.
Graeme Burk has done some more research:
We all know the story. Barry Letts cast an actress, initial work was done with her and then…she was dropped because she ‘wasn’t working out’. (Rumours abound that this means anything from she was terrible to she didn’t get along with Jon Pertwee to she got along a little too well with Jon Pertwee…) The identity of the actress has never been revealed, in spite of the fact that Doctor Who fandom has some of the best researchers on the planet. (They can find 40 year-old telesnaps but ask them to find an employment memo from 1973…hmph). Heck, I once tried to get the answer out of Terrance Dicks while we were both in a cab and very drunk, but he insisted that he didn’t know.I have reviewed the evidence, and I am pretty sure that Ms X must have been Fiona Gaunt.
Even this year  at the Gallifrey One convention, Barry Letts refused to name names, though he offered one tantalizing hint: the actress was bought out of her contract, which would have meant that she was paid for the entire season. This would have required approval from the Head of Serials and memos and such…and yet this has eluded our crack team of researchers.
Rather like determining the identity of Deep Throat there are some interesting theories. One theory goes that it was actress Fiona Gaunt, who played Helen in Letts and Dicks more adult (read: boring) SF series, Moonbase 3. Moonbase 3 and Season 11 of Doctor Who were being produced around about the same time, and being moved over to Moonbase 3 would mean that she didn’t necessarily get bought out of her contract per se, hence why no paper trail has emerged. And she was a dreadful actress (Moonbase 3 all but ended her television career).
My favourite theory was one that was conceived in a fit of silliness at Gallifrey last year: that they cast someone who’s now very famous. I mean, if you were Barry Letts would you really want to admit that back in 1973 you had originally cast Judi Dench as Sarah Jane Smith but sacked her?
Judi Dench is only 5'1" = 155 cm tall, so fails the criterion of Ms X not being short enough for Pertwee (quite apart from the fact that we are not meant to take Burk's proposal seriously). Tat Wood, in About Time Vol 3, suggests either Fiona Gaunt or Michele Dotrice, who fails on the same grounds at 5'2½" = 159 cm (and was in any case well established in Some Mothers Do 'Ave 'Em at this point). Susan Jameson might be a contender for Ms X on this score - she is 5'7" = 170 cm (of female Who companions, only the two Romanas were taller). But she would have had no problem with regard to her bust, as I think is clear from this still from her appearance in an episode of UFO.
I must say I am greatly enjoying her performance as a foil to Tom Baker's Doctor on the BBC audios by Paul Magrs - her portrayal of Mrs Wibbsey is almost the best thing in them.
I think that Letts' oft-repeated story that Ms X had been paid off must be a polite and tactical distortion of the truth - if it were literally true, Pixley and/or others would have found the paper trail by now. I believe that Fiona Gaunt was 'bought off' by Letts and Dicks giving her the female lead part in Moonbase 3. And while we cannot judge Fiona Gaunt's chemistry with Jon Pertwee, in my opinion she fits the other two criteria revealed by Elisabeth Sladen. Clive James described her as "a lushly upholstered young lady" in Moonbase 3; in this two-shot with the show's lead Donald Houston, it is clear that that she is at least average height for a woman if not a bit above.
Clive James has more to say about her cleavage in his review of War and Peace from the previous year:
‘Papa’s arranged a little dinner party for my name day,’ breathes Hélène, her piercing boobs heaving in a frock closely resembling a two-car garage: ‘I hope... you’ll be there.’ Pierre, valiantly played by Antony Hopkins, can only goggle, bemused. Except when the occasional voice-over supplies a brief stretch of interior monologue, goggling bemused is what Pierre goes in for full time. At Hélène’s party, during which her sensational norks are practically on the table among the sweetmeats, Pierre is asked to do a worried version of the bug-eyed act Sid James turns on when he is abruptly shoved up against Barbara Windsor.You may wish to make your own judgement:
Fiona Gaunt, playing Hélène, is the one on the right (and Antony Hopkins, at 5'8½" = 174 cm, the one on the left). Oddly enough, Colin Baker, the future Sixth Doctor, plays her husband in this story. Clearly there is some impressive corsetry going on here, but even making allowances for that, I think we have identified a plausible candidate who fits the clues given by Elisabeth Sladen as to Ms X's identity. Apparently Nothing At The End Of The Lane is to examine this question in their next issue, and I shall read their conclusions with interest. (Thanks to a commenter on an earlier locked entry for pointing me in the right direction on this.)
Edited to add, 10 January 2012: I was completely wrong abut this. The real identity of the non-Sarah Jane was April Walker.