As someone who has bought and sold a LOT of homes, I can now see why moving home is so stressful. While I totally appreciate how frustrating it is to get to your new home and find that the previous owners are still there, and only half moved out, all of the posters saying throw them out, call the police, blah, blah, are talking absolute crap, and were just trying to egg on the OP to be aggressive to people who were obviously already stressed, making the whole situation worse for everyone, including the OP.
The fact is, that on moving day, any number of things can and do go wrong. The original owners, may have had a sickness bug running through the family for the last week. They may have been dealing with a death in the family. They may have young children and no one to leave them with on moving day, so they've been getting under everyone's feet, and delaying things. The removal van could have had an accident, or a flat tyre, or a breakdown. Some people are even so poorly informed that they think they have all day to move out, but the fact is, if the person at the beginning of the chain has paid over their money at 9am, it really doesn't give the person they've bought from, time to have even loaded their removal van, so going along and saying 'this is my house now, you need to get out', is only going to make life miserable for all concerned.
I actually experienced this once with a couple of gay men, who bought our family home. They were first time buyers and so had very little to move, so on moving day when their solicitor told them their funds had been sent over, they drove straight over, and expected us to move out there and then. I had a young daughter, and the house we were moving from wasn't what you might class as a 'first time buyer's' home as it was quite big. We'd done all the preparation we could, but the removal van had been late turning up, and so only about half of our stuff had been loaded when they arrived. We also hadn't heard from our solicitor to say that funds had been received, so initially we told them they'd have to wait. We asked them to be patient, but one of them came in, all full of swagger, telling us that it was his house now, and we needed to get out, I explained about the removal van being late, etc. and that our solicitor hadn't yet received funds, so although his money had been sent into the system, the house wasn't even officially his, until it had been received by our solicitor's bank, which he didn't understand at all, so marched off to tell his partner what I'd said. A few minutes later, they both marched in with boxes in their arms. I asked them what they thought they were doing, and once again, they gave me all the bullshit about 'we've paid our money, etc'. I told them that we'd asked them to be patient, that there was plenty of time for them to move in, but moving their stuff in, before our removal men had finished, would likely result in some of their stuff, being picked up and put on our truck, and as part of our stuff was going into storage, they might not be able to get it back for several weeks! Only when I'd told them all this, did they realise that what I was saying made sense, and once they'd backed off, and gone to sit in their car, things went at a rate of knots to get stuff moved. We'd just finished loading the van, when the solicitor called to say that funds had just been received, so all of the harassment, and stress had been completely unnecessary.
So after such a long post, what I'm trying to say is, if we all practice a bit more patience, and given and take on moving day, a whole lot of stress could be avoided.