From my ILR and Naturalisation experiences, partners were not allowed (signs up and everything). Only those with a child seemed to be allowed up as it seemed they didn't want to separate a parent from a baby even if the baby wasnt applying. That being said, I went to a core centre not one of the premium locations and my understanding is that the service is "better" there (which is the incentive for paying more to go there vs. Paying for an out of hours appointment at a core centre) so it may be allowed. Worst case scenario, go with her on the day and if they tell you that you cant come in due to space or something, go get a coffee for 30-45 mins and meet her when she calls to say shes done. Just note that I dont believe you'll be allowed to physically go to the biometrics machine or desk with her regardless. My husband went to the appointment with me but couldn't come inside and I'm kind of glad he didn't because would've been bored just sitting there waiting and it meant I could read my book while still feeling supported because we drove to the centre together.
Best of luck
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