Who to contact to get licence early after driving disqualification?

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You will need to apply in writing to the court where you sentenced and provide all the necessary details like date of conviction and offence and reason why you're requesting your licence earlier. The 2 year rule apply from the date you were disqualified from driving, that is, when you ban came into force. In your case, it would be a month after the offence from the details you've provided.

Note that you may have to pay court fees and if you're application is successful, you will also have to pay DVLA to get your licence back. It's a renewal fee of £90 (at the time of writing) for drink driving offences and you should receive the licence within 3 weeks of receiving your completed application form (D1 form) for your licence.