UK travel ban;caring responsibility exemption, HELP!

Hello all, I am looking for anyone who might be able to help me and provide me with information regarding the UK’s newest set of Covid-19 restrictions.
Travel abroad has been barred except under certain legal exemptions, one of which is caring responsibilities or carer obligations.
My wife is a US national, residing in the United States. She suffers from chronic medical issues and she has legal disability status in the US. She is a recipient of social security disability income.
She recently had major abdominal surgery (her 3rd in the last 13 months) and due to my absence, the church she attends provided assistance and care in the immediate aftermath. But they are not able to provide ongoing care.
She receives case management from an assigned social worker because of her chronic disability and ongoing need for assistance.
I am due to fly to the USA in just a few weeks time in order to provide these caring services to her myself, as her legal spouse. I am supposed to be in the USA caring for her until the end of February.
My question is this;
What documentation or proofs do I need to have in order to verify that I am in fact eligible for the travel exemption? What do I need to provide our government in order to leave?
She has a disability awards letter from the social security administration detailing her status as permanently disabled and requires ongoing care & assistance.
Her pastor has agreed to provide us with a letter stating that she needed the church to step in and provide care in my absence but such care cannot continue to be provided long term.
Should I have her contact her social worker for a letter outlining the same information in regards to requiring ongoing care?
Perhaps contact her doctors and ask for letters from them verifying her chronic medical issues?
Any information would be extremely helpful.
Thank you

I think youmight have more problems with entering the USA as opposed to leaving the UK - perhaps a call to the US Embassy would help to clarify your situation ?