Yorkshire Dave
Western Thunderer
This I deduce is the head wall for the Westbound platform at the Kings Cross end. With the transposed Eastbound signal box being at the other (Finsbury Park) end.
Coming onto non-public/service cross passages shown on the GNP&BRly plan this could be a later dated plan as the other plan carries the full title of Great Northern Piccadilly & Brompton Railway.
I came across a YouTube video of an unauthorised access to York Road which in the later stages shows a brief glimpse of the alcove/doorway. From this it appears to lead into the cross passage. Any tiling would be carried around as far as the door frame as it would have been on public view.