The old stump and roots can be difficult to remove by hand - I've had experience of doing this when some willows (not cricket) were affected by Honey Fungus - ooh you REALLY don't want to get that.
Honey fungus is a spreading, parasitic fungus that lives on trees and woody shrubs. It is neither small nor a passing fad - the largest single honey fungus so far discovered is nearly 4 miles square (that is 2 miles along each edge) and is several thousand years old. It can be enormously destructive and is capable of killing complete woodlands. Honey fungi infect and kill woody plants. They do this by sending out bootlace-like structures called rhizomorphs which spread just under the soil at a rate of about 1 metre a year. Rhizomorphs can be hard to find so usually the only easily visible sign of honey fungus are mushrooms that appear in winter between November and January on wood (sometimes from roots only a few centimetres under the ground. The mushrooms appear in dense clusters, their caps are sticky when damp and tend to be a yellowish-brown. Young mushrooms are conical but they end up lowered in the centre as they get older. For the mushroom hunters among you, all Honey Fungus varieties have a white spore print. This is crucial for mushroom eaters as there is an extremely poisonous mushroom that looks similar and grows in the same conditions but which has a black spore print.
How does it kill?
If the rhizomorphs get through the defences of their victim, they grow through the tree and then rapidly encircle the cambium layer at ground level, cutting off the supply of sap to branches and leaves and killing it almost instantly. Infected plants such as trees, shrubs, other woody plants and herbaceous perennials suddenly start to die back, or leaves fail to appear in the spring. Resin can seep from the trunks of conifers. A real tell-tale is that plants under attack often flower and fruit better than they have ever done before. And then die. The roots and stems or trunks of affected plants are covered in mycelium, a lacy white fungal sheet. You find this by levering off a bit of bark at or just below ground level (a stout screwdriver is ideal). If there is a white layer and it smells strongly of fresh chopped mushrooms you have identified the cause of death. Having killed their victim, the rhizomorphs then feed on the dead wood which fuels their growth in search of another target.
Treatment.
There is no cure available to the amateur gardener for honey fungus but you can restrict its impact in your garden. Remove infected plants as soon as possible including as much of the root system as possible. If the tree is too big to pull then have the stump ground out until it is at least 8 inches (20cms) below soil level. This removes the food source. Obviously you should get rid of trees that have died for other reasons as well. It is also most important to keep plants healthy by mulching regularly with good organic matter. All plants have some defences and honey fungus tends to attack and kill plants that are stressed, diseased or damaged. The more you improve the quality of the soil in your garden, the healthier your plants will be and the more resistant to honey fungus attack. Quality growing conditions and good garden hygiene cannot be over-emphasised. Plants that are prone to honey-fungus attack can flourish in good growing conditions while those that are supposedly more resistant die in a year or two if conditions are bad.
For the sake of completeness here are lists of plants that are more and less vulnerable to honey fungus.
Prone to attack: Betula (Birch), Cedars, Cotoneaster, Cupressocyparis (Leylandii), Forsythia, Hydrangea, Ligustrum (Privet), Malus (Apples and Crabapples), Peonies, Prunus (apricots, cherries, peaches and plums), Rhodendrons/ Azaleas, Ribes (Currants), Roses, Salix (Willow), Syringa (Lilac), Viburnum, Wisteria.