I've tweaked the title to maybe prompt a few more people with more local knowledge than myself to have a look.
I've looked through Fairbairn (who I noticed popped up in the forums the other day for the first time) and Dunham and I can find no mention of anything up there, nowt on the old maps either.
The location you've marked is about midway between Redway Level and Hopeburn Shaft which are the only listed communications with Boltburn in the literature and then probably a good chunk to the east of those workings.
Dunham talks about three cross-veins at 3250ft, 7000ft and 8540ft from the engine shaft. Its very roughly in the region of the second.
He does go on to mention evidence for old workings of limonitic iron ore in the fell-top limestone near the course of the cross-vein, but I think that refers to the third one.
Short answer, no idea, look forward to seeing some pictures of inside.