Driving licence
So I've just had the letter from DVLA asking me to send in my current licence after notifying them of my MS. I will be sent a medical licence. That leaves me with no ID if I need it in the time it takes for the new licence to come back. I don't have a passport. It hasn't taken long. My diagnosis was only 22 days ago.

The bit that can take ages is when they contact your medics to get thier statements. When they have decided which one you can have they return your licence fairly quickly. Have they asked you to go to Specsavers too? If so maybe hold off sending them your licence till a couple of days after the eye test.
No they haven't asked me to go for eye test