No, you do not need a diagnosis, and you do not need a referral from a doctor to begin counselling with us. Many people book their first appointment without having spoken to anyone else about it. Others have seen their family physician, found it useful, and want somewhere to talk at greater length than a medical appointment allows.
A diagnosis is not a ticket you have to produce at the door. Counselling works from what you describe, which is usually more detailed and specific than any label. There are situations where a referral or documentation is useful for a different reason, such as certain workplace or insurance processes. That is separate from whether you can attend; your provider or employer can tell you what they require.
If you already have a diagnosis, bring it. It becomes part of the picture rather than the whole of it.