@texas Yes, the mini gel box can be used in the UK. It is just the power supply that must be compatible, as you mentioned. If you already have an electrophoresis power supply that you use then it should work with our mini gel box.
Just fyi, our electrophoresis power supply kit works with a 15V wall adapter. The one we ship with the kit is this one from Digikey Part # 237-1435-ND. The input range for the 15V wall adapter is 90-260V AC so this will work in the UK. You would need a plug adapter though. You can also choose to supply your own 15V wall adpater with this kit.
Hope that helps !