I witnessed a similar occurrence in East Midlands airspace VERY recently. ATC calmly handled the situation, vectoring another aircraft round and back onto the ILS track. No harm done but it appeared to be caused by someone taking off from a local field and not calling up in time to be told "remain outside"....
Hope the instructor apologised sufficiently in the telephone debrief; he was probably unaware of the concern he caused .... and checks his chart next time, oops.