Posted 04 June 2016 - 08:58 AM
I am puzzled by your comment about the fuse. It is illegal and dangerous, for very obvious reasons, to have one single fuse controlling both headlights, and no Mini was ever built that way. So attending to one fuse would not fix both lights unless the wiring has been illegally bodged by a previous owner.
The advice you have been given about checking the dip switch is correct, however a faulty main light switch would kill both main and dip.
You should have either no fuses at all in the headlight circuit on early cars, or 4 fuses, one each for left and right, main and dip. (Some configurations with 4 aftermarket relays may manage with 2 fuses for left and right, but that would be very rare.) Any other configuration is illegal and may invalidate your insurance, so it is important to check what is actually there and restore it to proper condition. It is a job that is not very expensive and should only have to be done once.
The other place where failure is common, due to dirt and corrosion, is the bunch of bullet connectors near to the bonnet lock. If you have access to a proper crinp tool I strongly recommend replacing them with something better such as blade connectors, with plenty of contact grease to keep the water out. Also, identify the earth wire from each light cluster, the black wires, and instead of having them join one common black wire back to the bulkhead, run seperate earths back to the body for right and left lights. Very much safer, and the way that later Minis were wired, for legal and safety reasons.