As well as visas citzenship and what have you.
It may also be worthwhile to think about Life Insurance.
Particularly if bad fortune occured within a short time of arriving in the UK.
Some policys may not pay out to non UK residents (The defintion of which can vary)
Also although most do make sure you have a bank account and proof of address and ID.
Do you have Bills in your name and in your joint names?
Otherwise any paperwork maybe much harder to navigate though.
Do you know where all the household paperwork is and does you both have Wills?
If your Loved one passed away it is a tough time but it is really worth spending a few hours making sure everything is ok. Which hopefully means as your prepared your not have to worry about it in the near future.