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A bit worried, yes.
Firstly you should at least clean it off the surface with a mould killing spray. You definitely don't want to leave that sitting there distributing spores into the air, it's bad for your health and the rest of your woodwork. When you are spraying/cleaning then use a decent mask because the spray and the mould spores can affect some people really badly.
To go a bit further you take off the beading that holds the window in, remove the sash cords and the window (tie the sash cords so the weights don't pull them through the pulleys then remove the staff bead that separates the two sashes you will find a little hatch which gives you access to the weights. You should treat the cavity where the weights live then put it all back together and when/if it doesn't come back restore the paintwork.
The tools you need to do that are :- a small pry bar, pair of london pliers (pump pliers will do at a pinch), sharp knife & hammer.
If it's buried deep in the woodwork of the interior of that frame you will need to consider replacing that wood or spending some time treating it.
It could be caused by lack airflow around the window, in which case you need to leave the window open more often and make sure the curtain isn't constantly in contact with that area.
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Thanks for the comprehensive reply, I don't think airflow is a reason as the window is always left open slightly and even when shut lets in a draft.
So builders have who did work on the property a few years ago have inspected the mushroom...
It turns out when the security bars were fitted to the exterior of the building, the guy who did it didn't consider that the basement of the house (where that window is) was tanked. Therefore he put a stud straight through the damp course, which is probably the cause of the problem.
Luckily its not my house and will be signing contracts on my new place by the end of the month.
Has anyone seen this before? Should I be worried?