It's not a question of how much in the main but where it is.
If it's cash and personal possessions then you don't need probate - but you may still need to inform the Inland Revenue.
If it's in a bank or stocks and shares, then each organisation has its own idea of how much it will pay out without probate - some are fairly generous, others can be very awkward even with very small sums. If it's a house, it depends on how it was owned and who it's going to.