As a toiler at the NHS coalface, allow me to predict how this will play out.
Let's look on the bright side, and assume that Wes really will tell hospitals that wards should be single-sex, but that they need separate, facilities for trans people, which don't require them to be on the ward of their birth sex (something that I would support in principle- my priority the safety and dignity of women, but I'd like a solution that doesn't distress anyone who IDs as trans).
Wes, as SOS for Health, issues this edict to NHS England, who, in turn, issue it to hospitals. There will not of course be any extra funding to implement it, so any costs involved will be taken from other patient services.
With no funding to build additional facilities, hospitals have to juggle with what they already have. How difficult this is will vary wildly, depending on how modern the hospital is. Hospitals built in the last 15ish years typically have all beds in en-suite single rooms. So the 'ward' is not a ward in the traditional sense: it's a group of rooms, more like a hotel corridor. It would be easy for them to designate an area as for trans patients as and when needed - the trans patient does not need to be in shared facilities with people of either sex.
But, for older hospitals, their only option is to use one of their scarce single rooms, which means one less for people with infectious illness/people who are dying/breast-feeding mothers (on wards other than the postnatal ones). If they can't free up a room, they will just argue exceptional circumstances, and almost certainly house the patient on the ward of their gender identity, not their sex because the NHS has been comprehensively Stonewalled. So, in fact, nothing whatsoever will have improved for women, even if Wes is currently telling the truth. Wes, like any SOS, won't care about that. He commanded, it was done. End of.