Okay, your sponsor letter is a bit too focused on unnecessary information and not enough on how you meet each requirement. I would refine it a bit. Also, I wouldn’t be so detailed with the information about your father - they don’t need all that info.
Also, the immigration service is notorious for giving incorrect information and bad advice, so while you would certainly mention your father’s health, I don’t know that UKVI would even look at his medical records.
Given that it is your father who is ill, and you are a U.K. citizen, there is nothing stopping you from returning to the UK to be with him while your wife waits for her visa, so they may not even consider the circumstances to be serious enough to rush the application. Not to mention, the majority of the processing time will involve your application sitting in line with no one having seen it yet, so likely no one will know that you have compassionate circumstances until the day the visa is issued.
For example,
To The Entry Clearance Officer,
I am writing to confirm my sponsorship of my wife [name] in her visa application to settle with me in the United Kingdom. I am a UK national who was born in the UK but I have been living in Australia for the last three years and I now wish to return to the UK with my wife.
We will be meeting the financial requirements using Category D: Cash Savings of £X amount. These savings are spread across X bank accounts and I am including 6 months of statements from each one.
Once the visa has been granted, we will be living at [address], which is a 5-bedroom house owned by my parents. In total, there will be Y people living in the property and so will not be overcrowded. I am including a letter of invitation from my parents along with their Land Registry document and their latest original mortgage statement [if applicable]
My wife and I met in a pub in Soho, London in April 2014, while she was on a [state exact visa type] in the UK. We entered into a relationship on X date. However, we had a 12 month break in our relationship from October 2015 to October 2016 [give reason why], but were still in regular contact. We then resumed the relationship in November 2016 [give reason why] and have been living together in [city, country] since April 2017. We got engaged on X date and got married on Y date in Z city, country.
We are returning to the UK because my father was diagnosed with metastatic melanoma in May this year and unfortunately, the cancer has spread more quickly than hoped. I have included my father’s most recent discharge summaries from ---------- and ----------------- as suggested from my email correspondence with the immigration service.
Please consider our circumstances when reviewing our application, as it is important for us to be able to be with my father in the U.K. as soon as possible.
Yours Faithfully,
Your Name
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