If he is a male at conception/birth his biology is fixed.
The fact that the sex was misrecorded and not corrected will not change biology and the SC ruled its biology not State issued paperwork which matter.
He wants to be recognised as a female while he is male.
If he was not a male he could not be excluded from female spaces unless he being female having modified his body to look male looked male.
You neatly demo why pronouns are important:
EA2010 does not have any specific provisions to protect people with DSDs.
6Disability
(1)A person (P) has a disability if—
(a)P has a physical or mental impairment, and
(b)the impairment has a substantial and long-term adverse effect on P's ability to carry out normal day-to-day activities.
Agreed the physical elements are there but the long term negitive impact is not.
If IK was British, she he would not have the protected characteristic of gender reassignment, because she he would does not have the protected characteristic of (female) sex, which she he does not intend would like to change but can not post SC. And if she he did decide to change it, she he would not need to invoke gender reassignment, or could get a GRC, because she he could alter her his original birth registration as the correction of an error but is very unlikely to do that, following which she his documents would correctly reflect he would be treated as having, and having always had, the protected characteristic of (male) sex.
Irrespective of her his actual sex, the Act would protect her him from unjustified discrimination if:
someone thinks she's he's trans, or
someone thinks she's he's male, or
someone thinks she's he's female
(perceptive discrimination)
And, under the Schedule 3 exemption from the ban on perceptive discrimination, she he could can be legally excluded from women-only spaces (just like a man, or a transwoman, or a bearded transman) purely because she he looks like is a bloke.
And she he can be excluded from female competition on any grounds you like (she's he's a man, or she's he's not a woman with a DSD - take your pick, because having a DSD isn't a protected characteristic).