Hi Debster, the bracket fungus may have been a secondary thing, so check if it was honey fungus which actually killed the tree. To do that, strip the bark off of the trunk at ground level. If you find a mass of bootlace-like threads running from the ground up the trunk, beneath the bark, that would indicate honey fungus and it would be inadvisable to plant another tree there or nearby. If you don't see anything like that and as long as you have the roots ground out, it would be relatively safe to plant another tree. Bracket fungi grow within the tree and don't spread through the ground, unlike the devastating honey fungus which will often go on to infect the whole garden (a single honey fungus can cover an area the size of several football pitches!)
This might be helpful http://apps.rhs.org.uk/advicesearch/profile.aspx?pid=180 - the photos are useful aids to identification, they show the 'bootlaces' particularly well.
If you scroll down there's a link which gives some of the trees and shrubs which are more resistent than some to honey-fungus.
It's a fungus - it exists - this tells you how it spreads
The fungus spreads underground by direct contact between the roots of infected and healthy plants and also by means of black, root-like structures called rhizomorphs (often known to gardeners as ‘bootlaces’), which can spread from infected roots through soil, usually in the top 15cm (6in) but as deep as at least 45cm (18in), at up to 1m (3¼ft) per year. It is this ability to spread long distances through soil that makes honey fungus such a destructive pathogen, often attacking plants up to 30m (100ft) away from the source of infection. extract from RHS Advice linked to above.