This law doesn't affect any of the rights or privileges of the Church of England, nor does it force them to change their doctrine, how they worship, and so on.
Not seeing how she can't sign this bill,
HL mk2.
From the bill
linky (1) A person may not be compelled to—
(a) undertake an opt-in activity, or
(b) refrain from undertaking an opt-out activity.
(2) A person may not be compelled—
(a) 10to conduct a relevant marriage,
(b) to be present at, carry out, or otherwise participate in, a relevant
marriage, or
(c) to consent to a relevant marriage being conducted,
where the reason for the person not doing that thing is that the relevant
15marriage concerns a same sex couple.