I'm really sorry, I was wrong. However, it's not just a blank refusal. If there are reasons why you want a name change without the spouse's permission then it can still be done.
So, if this is a case involving domestic abuse, then that would likely be sufficient reason for not needing the spouse's permission.
The relevant statute is The Enrolment of Deeds (Change of Name) Regulations 1994
Regulation 3(2) does indeed say that a spouse needs permission, but that requirement can be dispensed with if there is good reason:
3(2) In addition to the documents set out in paragraph (1), an applicant who is married must—
(c) show that he has obtained the consent of his spouse to the proposed change of name or that there is good reason why such consent should be dispensed with.
[emphasis added]
So you would need to include in the application a statement about the domestic abuse.
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But, just to step back a bit, I think that @LittleGreenDragons gives some very practical advice here:
"Would it be easier to change banks and then do a normal deed poll? If not, then open another current account elsewhere, do deed poll/name change, close Lloyd's bank account when safe to do so."
Opening a new bank account in her current name and then afterwards changing the name of the new account will likely be the easiest way of achieving what you are looking to do.