So if we were married and one partner needed medical treatment but couldn't consent - who would?
Doctors acting in their perception of the patients' best interests.
Usually this is what you'd have agreed to anyway (leaving aside issues like JWs and blood transfusions).
However, the fun can start when it involves DNR notices or their absence.
As others have pointed out, spouses don't have "rights" by virtue of marriage, but there's a lot of caselaw, custom and practice which says that there's a very, very wide window in which they'll accept a spouse's view. So the range of options a spouse can consent to, or not, on their spouse's behalf is going to be very wide.
It's not as wide as the range they'll accept when the patient themselves is giving or withholding consent (which requires sectioning to overturn), but I suspect that cases where a spouse's opinion is overridden are few and far between and mostly involve DNR.
I would further suspect that as you go down some hierarchy of parents, children, unmarried partners, etc (in some order) the range of options doctors will accept from you before they mutter about going to court is progressively narrower.