Found this on an Amazon review, tried it and it worked!!!! only took me 2 years to solve this :-(
This was a great radio when it worked but it’s been sitting on a shelf with a faulty on/off button for over a year. Roberts charge £40+ to fix it and there are no fixes on the internet (so far!). Today l decided to have a play with it to see if I could get it working...I now have a radio which is on when connected to the mains but the on/off switch still doesn’t work so you need to turn the electricity supply to it off to turn it off. Purely by chance I discovered this fix which is dead easy to do. First disconnect from the mains supply and take the back off. All the screws are arrowed and don’t miss the one in the battery compartment. Next to the green on/off switch on the inside there are three wires connecting it to a circuit board. They are orange, black (in the middle) and red. These wires are about 2 inches long and have small white plastic connecting blocks at each end. Anyway I discovered that disconnecting the BLACK wire bypasses the switch entirely. I removed the end of the wire from the plastic block which plugs into the circuit board and put some insulating tape on it but snipping the black wire and putting insulating tape on the ends would have the same effect. If you were going to throw your radio out, try this, you’ve nothing to lose.
Dominic, June 2020