When the load won't fit, don't start pushing
A situation where the load won't fit in the van can almost always be solved, just not by force. The worst reaction is to cram things in, leave an item sticking out and hope for the best. Stop for five minutes, unload what you have already loaded badly and go through the options in the order below.
First try a different order
Most failed loadings are a problem of sequence, not volume. The longest and heaviest items go in first and against one wall. Wardrobes, doors and table tops are carried upright along the side, not flat on the floor, where they take up the whole area. Only then do the boxes go into the gaps.
Take apart what can be taken apart
Table legs, shelves, bed headboards and wardrobe doors make a huge difference. A dismantled wardrobe takes up a fraction of the space of an assembled one. Put the screws in a bag and tape it directly to the part it belongs to. Ten minutes with a screwdriver will save a whole second trip.
Use the height
A van has usable space right up to the ceiling. Light and soft things go on top, and boxes are stacked in columns. Just make sure there is nothing heavy at the top and that nothing can fall against the rear doors.
Unload what doesn't need to go now
Divide your things into essential and postponable. Garden furniture, seasonal items and boxes of books can wait. Load what you can't do without in your new home and collect the rest next time.
Try turning items
Most bulky items have one position in which they take up the least space. A sofa stood on its side, a mattress leaned against the wall, a table top upright. Before you decide that something won't fit, try the item in all three positions. Often only a few centimetres are missing, which you can gain with a different orientation.
Empty what you are carrying full
A chest of drawers with its contents takes up the same space as an empty one, but weighs several times more. Clearing out the drawers takes some work, but then the units can be stacked on top of each other and carried by one person. Conversely, fill empty baskets, pots and crates with small items so you are not transporting air.
Load through the side door too
The sliding side door makes it easier to stack things in the front part of the van. Long items get in more easily from the back, but you can stack boxes in the front third much faster through the side, without climbing around on the load floor. Just check that cars parked alongside are not in the way.