So what does 'processing' mean?
If it simply means scanned onto their system, then don't expect anything to happen soon.
I applied on the 15th July.
My application was scanned on 24th August, 5.5 weeks later and it took them until 31st August to cash my cheque.
As of now (09/09/21) nothing. Complete silence.
I even called and informed them that I had spoken with a Medical practice who were under contract to the DVLA and that this practice had told me their was no issue in making an appointment for a medical. Once they had received the relevant paperwork, I would be able to get an appointment within a couple of days. I asked for this to be noted on my file and that this was the practice I preferred as it was easy for travel.
No idea if they did that or even listened to me seriously.
TBH, I think they are simply working through this admin part of the process in date order of the backlog. Until you get a letter from them telling you to make an appointment to see a Doctor, then nothing will speed this stage up.
My real fear is the time taken between my medical, the results being available and checked by a DVLA medical team and then waiting to find out if they will write to my GP.
I thought that's what "processed" meant too, it sounds very vague and beaurocratic I think because it's DVLA and we all have our experiences with them.
I assume it means scan onto system, sent to the relevant department and then wait then wait some more ... for it to be looked at by doctor / case manager then decision made as to the way forward.
Then wait for medical, results etc etc - my fears are the same as yours.
The medical dept have had my GP report since August 10th.They may well ask for another at the end of the process.
The order of things seems to be different for different people according to what I have read on here.
Some people have been asked for GP report only after the medical.
I was written to by DVLA saying they were writing to GP for report before they could make a decision regarding my fitness to drive.
I was hoping (though very doubtful) this was a positive as it may have been a suggestion of licence being issued without medical and it would be a speedy process but I don't think so now.
Like you I fear a very, very long delay, possibly well into 2022.
I waited exactly a year (last time) for my licence reissue purely because of a mistake the DVLA doctor made simply by not taking a note of a phone call to my GP. It was completely their mistake and I had to go back to the beginning of the whole application process - completely new application filled in, GP report, wait for medical etc etc.
DVLA are a nightmare to deal with in my experience.