A few days ago I was politely told I should arrive 3-4 hrs before flight at check-in, having been delayed en route to Heathrow and getting there with just over 1.5 hrs to spare for the 15.05 (economy seat, flight was half empty so didn’t matter in the end). Implication obviously that it’s open at least 4 hours before.

As an aside the 380 was so empty they closed the front 2 sections of economy completely. I was bumped back to row 80. To balance the cargo.