Можете попробовать написать вашему MP. Ниже привожу выдержку из ответа от MP, но я не пользовался этой опцией.
As a constituency office caseworker, I cannot directly expedite applications. If you have any documents that show an urgent factor to your situation, please send them to me (please keep it under 2 MGB and include a certified translation in English if it’s in another language) so I can attach it to this application. This may include documents that could relate to issues with education, work, health/medical, death in the family, or other humanitarian, hardship, or compassionate grounds. I can't guarantee, but I have seen this expedite some cases. For what type of specific documentation to send me, in my experience the best evidence to hopefully expedite it would be something like a doctor's note (or other medical professional), where they explain how this delay is directly jeopardizing your health/wellbeing (and/or perhaps that of another family member who is also affected by this). I've even seen notes from professionals like a psychiatrist or counsellor that have sometimes made a difference. Also: documents that show a financial loss or hardship that are directly due to this delay might also help.