hi everyone, i am just wondering, as many people on holiday, is this the reason HO might taking more time on processing the visa

My wife has done the biometric on 15th july in one of the HO enquiry office for tier1 dependent visa , she is still waiting, I know its not too long as HO takes 4-6 wks but some people get the approval within 2 weeks and i thought HO processed application quicker these days.
Now becoz of my wifes mother's bad health and some family reason, she really needs to travel. Can i request home office by sending a letter to do quick processing the application?
any response from you will really help..please share your suggesstion or experice in same situation.