Obtaining a grant of probate does not seem to be compulsory, so how would the executor of a will decide whether to apply or not?
Generally it depends on the size of the estate. Relatively small amounts due to an estate from banks and building societies may be payable without an executor being required to produce a grant of probate, although some may require to see one. And cash and personal effects can be distributed among relatives and beneficiaries as long as they can all agree. But an executor will need a grant of probate to deal with larger sums, and to sell a house, for instance. Bear in mind however that sums of money in joint accounts, and houses in joint names, will pass automatically to the survivor and so won’t be included in the estate.