Wiring a car radio with two power sources
You are apparently located in London, and there are any number of electronics distributors which will serve you. Digikey and Mouser are both reasonable companies, and I'm sure there are more. Go to their web sites and you can do product searches to find diodes that will work for you.

Your wiring problems are readily resolved. As you suspected, you can use diodes, something along the lines of 







simulate this circuit &ndash; Schematic created using CircuitLab

D2 applies power to the radio when the switch is closed, and also to the LEDs. When this happens, D1 prevents the battery voltage from flowing back into the switched ignition and getting to the wipers. Likewise, D2 prevents ignition voltage from driving the LEDs. If the ignition and the battery are both applying power, whichever has the higher voltage will do the work. If one starts to drop (such as the radio discharging the battery) the switchover will be seamless and you won't even be able to tell it's happening.