If your estate is very small (typically less than £5,000), your heirs may be able to claim their inheritance without formally applying for probate. Many banks and others will release relatively small sums without needing this, though they will usually want to see a sworn statement explaining the situation. They may also ask for an indemnity, making whoever claims the money liable if they were not in fact entitled to it. Take advice if you are not sure.
If you left a will but did not name the executors, or if none of your named executors is willing to act, then one of the beneficiaries under the will can apply for probate as an administrator. If you did not leave a will at all, members of your nearest family will inherit and can apply for probate. In both cases, there are rules setting out the pecking order for who can apply.
All this can add an extra layer of confusion, delay and potentially conflict. It makes much more sense to make sure that you do leave a will, naming your executors.