I have had both packers which was ideal when I had a newborn. They come the day before and pack everything in no particular order and usually will take your beds apart on the day.
More recently we did diy packing and it was much more organised but obviously more work ourselves. We paid our moving company for boxes which they dropped round in advance. I also brought some rolls of bubble wrap and large sheets of paper for wrapping delicate items. Our Oving company provided massive bags for mattresses on the day and special padded bags for TV's.
We had to pack everything, empty the loft and shed. Take apart furniture. Unplumb the washing machine etc.
Top tip.
I would really recommend getting a tape gun and both normal packing tape and some which says fragile on it. And a large roll of cellophane wrap which eas great for wrapping things together e.g. all garden tools, brooms and mops etc.
Start with non essential fragile items e.g. wine glasses, ornaments etc. Then small pictures which will fit in boxes. Large ones they had bags for.
Some movers provide hangar boxes for clothes. I just picked everything off the rails, hangars attached and laid it in boxes.
I brought vacuum bags for spare duvets, pillows, coats, garden cushions etc.
Put heavy items like books into smaller boxes as they are easier for movers to carry. Save the big boxes for large odd shaped items.
Get suitcases to pack for your last few days so that you can pack everything else in the house, all the bathroom cabinets etc.
Make sure you leave cleaning supplies out.
Don't forget to defrost your freezer before moving day.
On the day, don't forget to take note / photos for metre readings at your old house and the new one.