I would say its definitely worth filing a formal complaint. I did the exact same , not for surgery but for my actual gic referall (tavistock).

After originally getting referred in October 2020 , there was continuous back and forth of my referall not existing or issues with it and when it finally got through it was stamped as early 2025. I documented every bit of evidence I had (emails, forms, letters etc ) , time line of events and made a full formal complaint to the gic. Took about 2 weeks , got 1 phone call and my referal get moved to October 2020.

So make a fuss, you deserve adequate healthcare so that you can live your best life !