Ring the sorting office that has responsibility for the post box that you used.
Many years ago, I posted off my car tax but forgot to put the address on the envelope. I realised my mistake just as I let the letter drop out of my hand. I rang the sorting office and explained what happened, the guy took my contact number and rang me when the letter surfaced. I had to call round to the office and he opened the letter in front of me - saw my details inside and allowed me address the letter and off it went.