Kim Walmsley, 49, said her 23-year marriage was declared illegal and she was forced to return from Australia after she could not renew her passport.
Her troubles began when the registrar wrongly recorded her as a male after she was born in February 1965.
Okay, so there are two totally separate issues here - the bureaucracy and the church. Now, nobody expects sense out of any bureaucracy and nobody expects sense from the Church of England on matters that could be considered, from even a hypothetically reductio ad absurdum conservative point of view, to have anything to do with sex.
As far as the bureaucracy is concerned, a transsexual would be entitled to a "certificate of gender recognition". Mrs Walmsley should be entitled to a "certificate of sex and gender recognition". Or just "sex recognition". So that's settled.
As far as the Church is concerned, their error is far more egregious. It should not be worried about matters of bureaucratic incompetence or, in fact, bureaucratic recognition. Given that the Church's current position is that marriage is between a man and a woman - Section B, Canon 30, paragraph 1:
The Church of England affirms, according to our Lord's teaching, that marriage is in its nature a union permanent and lifelong, for better for worse, till death them do part, of one man with one woman, to the exclusion of all others on either side, for the procreation and nurture of children, for the hallowing and right direction of the natural instincts and affections, and for the mutual society, help and comfort which the one ought to have of the other, both in prosperity and adversity.
And Kim is clearly a woman (she's given birth to five children) and, Jack is a man, then the marriage is clearly canonical, regardless of the failings of the English Registry system.
Edited to add: reading elsewhere, Kim clearly has a case for an amendment to the register under s29(3) of the Births and Deaths Registration Act 1953:
An error of fact or substance in any such register may be corrected by entry in the margin (without any alteration of the original entry) by the officer having the custody of the register, and upon production to him by that person of a statutory declaration setting forth the nature of the error and the true facts of the case made by two qualified informants of the birth or death with reference to which the error has been made, or in default of two qualified informants then either by two credible persons having knowledge of the truth of the case or, where it applies, in accordance with section 29A of this Act.
Noting that s29A does not apply in this case (it is restricted to mis-identification of the father), then two qualified informants (in accordance with s1(2) of the same Act). Her parents would do, if they are still alive (and she's 49, so it wouldn't be abnormal) or two credible persons. I would suggest any of the obstetricians or midwives who oversaw any of her pregnancies or births or any gynecologist would do.
Now, this would not alter the initial in-correct registration but it would correct it and allow her issue of an accurate birth certificate and, providing the Church wasn't insanely stupid (I'm not offering odds here) belated re-recognition of the validity of her original marriage.