Judging by the second picture it is dry rot.
You don't always get a fruiting body - I've seen plenty of rampant dry
rot and not a mushroom in sight.
You do often get the stringy white rhizomes - particularly visible
when you cut out the infected wood - it runs along between the brick
and the wood.
by law you are meant to cut out all timber 1metre beyond the any
evidence of the dry rot and replace.
The adjoining walls should be treated and treated timbers used in the
repair.
You can be held responsible if at a later stage your dry rot invades a
neighbour's property so it is especially important to properly deal
with any dry rot on or near a party wall.
dry rot spores lie dormant for many years/decades waiting for the
right conditions ie 40% moisture or above