Assuming that DVLA sent the letter to you (second class I expect) on the same day they wrote to your GP then yesterday was the first day that the GP practice could have received the letter.
Whilst you are anxiously looking for a letter from DVLA to arrive, your GP practice isn’t!
Out of the £96 you pay for the medical, none of it goes to DVLA, it is kept by the doctor as an examination fee and to pay for the
CDT test.
If you have to do future medicals then DVLA cover the cost out of the £90 you pay for the licence renewal fee. Also out of that fee they have to pay your GP for filling in the form.
It isn’t the huge money spinner you think it is.