Sorry to hear of your problems with anxiety. Anxiety can present itself as a number of different disorders such as Generalised Anxiety Disorder, Social Anxiety, Agorophobia and Panic Disorder etc. Sometimes they occur alongside other mental health disorders such as depression or personality disorder.
Your GP is the normal gateway to talking therapies such as CBT. He can refer you to a therapist through the NHS, albeit there may be a waiting list. The service is called IAPT (Improving Access To Psychological Therapy). It can include treatment programmes of one-to-one therapy, counselling or group therapy. Formerly, IAPT was solely based on CBT (Cognitive Behavioural Therapy) but it now employs other types of therapies such as Humanistic Therapy, Psychodynamic and Integrative Therapy etc.
It's a good idea to know a little about the different types of therapies and how they work/which might be most apt for you, so you could ask your GP about that. I wondered why you were focused on CBT? (Not that it's necessarily a bad idea). CBT has been largely used by the NHS arguably due to its relative cheapness to provide and it being measureable for results - not because it is 'better' for the job (nor is it necessarily 'worse'). This doesn't mean that it's inferior in any way as it's very good for some things, for example addiction, it is also used widely for depression and anxiety. Sometimes however, there is a need to explore more deeply into a disorder as opposed to what some deride it as - a 'sticking plaster' approach. The bottom line is that some people respond well to certain therapies while others need something different. Good luck.