If you have your RN which you should have received via text, call NHS Fleet and request to know who the leasing company is. This might be predicated on the customer service agent's willingness to divulge that information #fingerscrossed.
The leasing company gets weekly updates from Tesla and should able to provide you with your estimated delivery date. Alternatively, you can speak with Tesla customer service, they are quite helpful.
It took me a lot of back and fort to gather all my info, only thing I don't yet have is my VIN but I will be drilling next week to try and get that also.
Hope this helps and good luck