I wish to remove some tall ladders from our existing kitchen and replace them with a worktop and underneath space for two free standing appliances. Do I need to add a separation panel between the two appliances or is a 130 cm worktop supported by end panels safe to fit two 60 cm wide white goods with no support in the centre?
1300mm will be OK until somebody stands on it to change a lightbulb or catch a spider, or sits on it for some reason. It will then dip, bend, and possibly crack.
But you can put an intermediate supporting panel, or a narrow towel and tray space, or wine rack, between the two appliances, fixing it to the floor, wall and worktop so it doesn't get knocked out of place. As a minimum you should put a ledger board or batten against the back wall to support the wall edge of the worktop. Any movement here will crack the seal with your tiles or splashback.
Dishwashers are exceptionally deep appliances so you may need to have the worktop little higher so the dwr doesn't hit the batten. They don't even leave enough room for a plug.
@PigletJohn Thanks, I will screw some timber to the wall to support the worktop, then. We haven't got the room for a wine rack or tray space between the two free standing appliances. The worktop will be an extension of our existing 65 cm plus deep worktop, so there will be enough room to fit a dishwasher and washing machine. I was brought up never to climb on or sit on furniture and fitments but to use a stepladder or a chair. I intend to teach the same to my child and her friends.
you might also be able to get a matching "pillar" to improve the appearance. They are usually available to match natural wood and painted doors, I don't know if there is a "general purpose" pillar in white or something.
A flat "board" will be adequate, though, but it must be fixed so it can't move or tilt.