Posted: 26/09/2015 at 15:54
Yes, it's mycelium (the main part of fungus) but it is NOT a problem. Fungi are essential in a garden as they break down woody matter which nothing else can do. All you need to do to is to dig the area over and add as much manure and compost as you can and your new border extension will be fine. Honey fungus has black root-like rhizomes (aka 'boot laces') and there is no evidence of that in your photo's.
There do appear to be a few couch grass roots though (white) so I would get all of those out while you are digging the area over.