A few years back I was on multi-drop and got to a company in Coventry. I pulled in and there were two artics waiting so I asked if I could go first as I had four pallets. They both said ok as they had full loads, but the forkie wouldn’t have it, they were there first and would be tipped first. Phoned my firm and was told to pull out and carry on with other drops.
As has been said delivery point staff decide who goes first.