If the person who died has left a will, it is the responsibility of the executor to administer the estate. It will depend on the value of what is left and how it is held as to whether probate is needed, eg: whether it is property or accounts or shares. Probate is a court order which can be required to release the assets. If there is no will, how the estate is distributed is set out in the rules of intestacy and a very similar process to probate may be needed.
The person responsible can choose to do all the work involved personally but the decision needs careful thought as it can take up to a year or even more to administer a complex estate, especially if a property has to be sold. Professional help is available from solicitors and specialist probate services provided by trust corporations.
It is important that every person has a will, both Islamically and according to British law. More information about creating a compliant will can be found at https://onlineislamicwill.co.uk.
As with all professional services, do ask about the terms and conditions of the service and how fees are charged before entering a contract.