@LiamO_Dell is right in saying that the DWP will fast-track cases where there is terminal illness (usually a form DS1500 would have to be provided for them to do this).
But also, contrary to popular belief, the DWP decision-making department is staffed by humans, who are able to prioritise their work how they see fit. It is uncommon for them to take pity on claimants where there is no terminal illness, and it may be the case that the medical assessor's requests for the matter to be expedited fall on deaf ears, but certainly it is possible.
From the perspective of working in benefits law for a while, I can think of many occasions where I have persuaded decision makers to look at things more quickly, so presumably medical assessors could do this if they so wished...
I hope they do for you!