Time is getting late and I don't know if the OP will still be reading this.
However, I cannot comment on your boiler problems but regarding your Landlord entering your premises without your permission I can tell you is strictly illegal. My daughter had this issue with a previous landlord, she would come home sometimes and find her mail neatly stacked on the hall radiator cabinet. She questioned her boyfriend, (who had a spare key but did not live with her at the time). One day when she would normally have been out but was at home because her car was in the garage she heard someone opening the front door so grabbed the phone and went into the kitchen. Peeping through the door she saw her landlord entering the living room. She was so mad she didn't think and confronted him asking what the hell he thought he was doing. His reply was that it was his property and he had the right to enter whenever he wanted to. As soon as I heard I contacted the police who said they treat such incidents as burglary and would always prosecute. The only time a landlord is allowed to enter a property is if their is imminent danger to people or the structure such as a fire or flood. Under no circumstances, including a tenant being behind with their rent, is a landlord allowed to enter without the tenants permission. I immediately changed the locks and then went round and told him in no uncertain terms that if he tried to enter again I would have him prosecuted and that I had already lodged a complaint to this effect at the local police station. He never tried again and would always phone first if he wanted to know anything. If you have any doubts about what I am saying just phone your local police station and explain you are seeking advice about this type of situation. They will confirm what I have said. If he says the boxes are not his then tell him you are going to open them and do with the contents what you see fit. If they are his he will try to bull$hit you into handing them over. Ask for proof that he is the rightful owner or you are considering taking them to the police as lost property.
Hope you get the boiler sorted soon