Sorry about your Father.
I went through easter last year when my dad died.
If the insurance is running out I’d say get rid of the car as soon as possible.
If it’s run out then get it temporarily put on your insurance so that it’s legal.
Don’t bother transfering ownership. Just write on the log book when you sell the car that your father is deceased. The DVLA is only really interested in the new keeper anyway.
I took my dads car to wewantanycar just to gid rid. As long as you have a copy of the death certificate selling it shouldn’t be a problem.