cant quote people but infairverona, welcome and well done for seeing the GP. the service wont diagnose you with anything but it will be clear to whoever is assessing you, what your needs are based on the answers to your questions. essentially these types of services will either offer you counselling or CBT... if something traumatic has triggered it then you might get counselling but usually it will be CBT, which will address both the anxiety and any underlying depression.
Secondly, I wouldn't jump straight into it, but if they mention that there is either group or individual, I would bring up at this point that you would rather 1:1. you are well within your rights to do this and this choice will mostly be respected. tbh if it clear that your anxiety has some sort of social element then they may just put you straight onto 1:1. hope this helps somewhat.