My God the world has become a horrible place. People honestly can't wait to jump in and accuse the OP of trying to somehow profit from the estranged relatives death . !
How about for ONCE people try and answer a question helpfully. Or say nothing ! It cost little to be pleasant.
When someone dies without a NOK then the local council bereavement services get involved. They will normally try and track down a relative.
If you are the only living relative then you absolutely MAY go to the home and look for a Will. If you find one and it names an executor then that is time for you to inform them and to back off. It is the executors job to arrange a funeral, gather in all monies, apply for probate if required and to distribute bequests to the beneficiaries. Executors can be private individuals or a firm of solicitors.
If no Will then your relative has died 'intestate' and you as the NOK can apply for letters of administration . If the uncle has any spouse, civil partner , children, grand children, great grandchildren, parents or siblings alive then they ALL take precedence before you. However if this is not the case then you and your brother are the sole beneficiaries of the estate.
No need for a moment of guilt. If he had felt that strongly about it he could have written a Will leaving it to the donkey sanctuary. Which of course is your prerogative too. !