Xylaria spp.

Yes that looks ok too. As it says on EOL - similar to Xylaria polymorpha but it's thicker and not as branched. As yours shows no branching at all but looks relatively thin this simply highlights the problems of IDing fungi from photos. Yours might be a 'young' version of either. The accurate thing is probably to mention the options in your notes but put the scientific name at Xylaria sp.

I spotted this today (yet to upload photos) and am pretty sure it is young Candlesnuff Fungus: http://eol.org/pages/1017301/overview

I think there's a good chance this is Xylaria polymorpha - descriptions include reference to the whiter top parts. http://www.wildaboutbritain.co.uk/gallery/showimage.php?i=42520&c=8&orderby=dateline&direction=DESC&cutoffdate=-1

Chester has it. Some of these are commonly called 'Dead Man's Fingers' ( but then so are several seaweeds and plants )