I am not a lawyer.
But my understanding is that under English & Welsh inheritance law, UNLIKE MANY OTHER COUNTRIES, a person can leave in their will what they own to whoever they want. There is no legal obligation to include living spouse, ex-spouse or children in the will. This may not be a wise move, but there is no obligation to make provision.
If your father dies intestate/without a will, then his estate/assets are distributed to a strict formula/hierarchy of family relationships determined by English & Welsh inheritance law. This means that should your father’s share of the house pass into his estate & he dies intestate, his living spouse will have first call on his estate.
Should you be in Scotland, then inheritance law there has different conditions.
Bluntly, does your father have capacity to undertake changing the tenancy conditions, &/or making a meaningful, useful & fair will??
Should he not have the capacity to instruct a solicitor to set up a legally binding document & his wishes waver, then I read your post as from someone looking to find a form of resolution & put in plan what YOU find fair & morally acceptable.
Amazingly, many people in this country who have children, own considerable assets etc do not have any will or what they have is either out- to-date or invalid wills, so your father is not unusual, & the dilemmas & family feuds you anticipate are the stuff of many a long standing grievance dragged through courts etc. So Waita you are not alone.
You are not obliged to put right what your father choses to do in his lifetime. This is critical & key. Whilst anyone has this sense of obligation on behalf of another, then they are an easy target for others who wish to exploit their uncertainty. So put aside what others think they may expect from you. That’s their opinion, not your father’s. It is not your job to be the peacemaker for a bunch of adults who have made their choices over the years. Indulging in this role will bring you no greater love & many years of stress, unhappiness & conflict.
This is the lesson for us all: if you want your wishes carried out when you die then get thee to a solicitor to make a will, otherwise things will get done as the law stands. Same applies to paying tax on yr estate.