Once a class one expires it reverts to a class 2 which is fine for training.
So after you have it, you will be good for 60 months up to aged 40 and 24 months until your 50 for training.
The only time it needs to be current again is for the issue of your license. At this point you will be about to be heading off for the sim and will be requiring it because you will be flying the line in the not so distant future so need a class 1. At this point BA have company doctors who will get it current again with no great hassles.
Getting the initial one is a complete ball ache compared to getting it renewed. Get it done ASAP don't hang around and risk you getting put back an intake because you don't have it.
It also means as well that those unfortunates that have issues can get them sorted before there slot comes up. There will be some that fail the medical.
Personally I would be on the phone tomorrow to book one.