As obvious as it seems, a thorough search should be carried out of the deceased’s residence. It is worth checking the property, including any places where the deceased may have kept all of their paperwork, or perhaps in an attic or other storage room.
If the Will cannot be found in the deceased’s property, and you are aware  the deceased used a particular solicitor during their lifetime, it may be that the solicitor is storing the original Will or a copy of the Will for the deceased and so it is worth making enquiries with them. If the firm of solicitors is no longer practising, the Solicitors Regulation Authority may able to assist in ascertaining where the Will is being stored.
Less frequently, banks store Wills for their customers and so it is also worth making enquiries with the deceased’s banks.
Finally, you can ask a company to carry out a Will search for a fee. This can identify where the Will is being held and by whom. However it is not compulsory to register a Will and so a Will may be in existence but not return any hits on a Will search.