Check to see if there are shorter waiting lists at other hospitals in your area. (Your GP can change your referral if there are).
To do so, go here
https://www.nhs.uk/Service-Search/Hospital/LocationSearch/7/Hospitals
and enter your postcode.
On the next page, click on the name of your local hospital.
Then click on 'Departments and services'.
Click on 'Ear, Nose and Throat'.
Click in the orange box labelled 'Compare waiting times . . . '
ENT waiting times are shown as 'Up to 17 weeks for 9/10 patients' for most of the hospitals around here.
At least your wife has got a date though. I've been on the waiting list for a prostate operation for nearly 10 months (having been told my case is marked as 'urgent' on the system), with no indication of a date for it yet.
I doubt that a referral from an A&E doc would speed things up for your wife. I ended up on the waiting list for my op after ignoring my prostate problem for far too long and ending up with an emergency admission into hospital at the end of January. So my referral was actually from a hospital consultant, rather than from my GP. (The hospital sorted out my immediate problems after a 5-night stay but I didn't end up any further along the waiting list to get the underlying cause of my difficulties dealt with).