The first time you contact the moving company to remove offices, you need to tell them what you mean. That way, they don't have to guess what to do. You also need to be very clear about what part of the job you will be doing. When you pack the boxes, make sure the moving company knows. If you plan to repack some items and repack others, re-clarify your instructions. They may need to re-evaluate their work, which is unlikely to make them very happy.
If you are considering a quick move at your local office, consider renting a smaller van with a driver who will also load the van. If the office is a smaller office and only moves a block or two, a smaller van is an easy way to keep things moving for a few days.
If your office needs to stay open during your activities and it's a short distance away, you can tidy up your office and put items that won't be used for several days in a separate location. Then the company of commercial removals such as https://www.woollcotts.co.uk/commerical-removals/ can start moving these items and placing them in the right places. On weekends, when the office is closed, the moving company can complete the move.
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Keep in mind that moving companies may have fixed hours of work during which they move goods at normal moving costs. If you ask them to provide their service before or after a certain time, they may charge overtime compared to normal hourly rates. This also applies to moving over the weekend. So, if you plan on moving the short distance to the office and don't want to waste company money, you need to plan carefully.