The washing machine is no problem as that has a delay setting. But the cold fill dishwasher does not. So, following a tip I saw online, I bought a TP-Link Tapo P105 Mini Wi-Fi Smart Plug from John Lewis. (£9)
This works on your wi-fi and your smart phone. You don't need a hub, but you do need it to be within reach of a 2.5g wi-fi source.
To make it work, you have to use a little trick. You start the dishwasher, then almost immediately turn off the plug using the app. Then you set the delay on the app so that the plug comes back on just after 2am. When the power is restored, the dishwasher resumes its cycle, which it completes within the cheaper period.
Using the separate Bright app on my phone, which shows the power consumption in 30-minute time slots, I can see when the machine is drawing power to heat water and dry the dishes. So, I know it works.