Hello Sarah - we can't advise you on what you 'need' to do in such cases and very much something to seek wider legal advice as appropriate
We deal with the legal ownership and if one of joint legal owners has died the legal ownership passes to the survivor to then deal with as appropriate. In such cases some will simply update the register re the death whilst others might transfer the legal ownership to new joint owners
Once you have decided what's best/needed then our online guidance can assist -
HMLR Guide: Start - External · HM Land Registry