You're using MR16 50W 12V Halogen Flood Reflector Light Bulbs is my guess. Some of these light fixture for these light bulbs have a small transformer (4 wires - 2 pri (blk & wht color) & 2 sec -- about 1 inch x 1-1/2 inch x 1/2 inch) for each light bulb. They cost as much as a light bulb (maybe more), My guess is this one was on its way out and is now open circuit.
The circuit breaker is a dangerous place, and should not be opened without proper safety training. Although a handy person could complete the repair, I would suggest hiring an electrician to handle this for you. But, since you rent, you really should have the owner handle this issue. I suggest leaving the breaker disabled until a repair is made, and that a repair should be made soon (in the next few days).
1) It's most likely that the particular circuit breaker is failing (no longer making good contact). Other possibilities include loose wiring (much more likely for aluminum wiring).
2) As mentioned above, the QP breaker is fairly easy to replace. However, you as a renter should NOT replace it yourself. People unfamiliar with the dangers of electricity should NEVER open up their circuit breaker panel. Note that it may be impractical for you to de-energize that panel, so the repair could not be made reasonably safe. If you do choose to do the repair yourself, turn off the big breaker at the top first, but note that there still will be lethal voltages in the circuit breaker box.
There may also be other issues that need to be addressed, such as loose wiring, which may not be obvious to the casual observer.
3) The small 20A QP breaker costs a few US dollars. The 200A one at the top may cost about US$60. There is a small chance that the breaker box itself is damaged or wires need to replaced, which would increase the part cost somewhat. Also, due to code changes, you may now be required to replace the 20A breaker with a safer type (AFCI), which would be around US$30.
Best Answer
The UK uses fused plugs because instead of using individual spurs or "home runs" rated at the receptacle rating to feed a few outlets at a time, they put all receptacles on a single "ring main" circuit that can provide more current (32A is typical) than appliances and their cords can handle (16A max, although smaller is common with BS1363 plugs). It has nothing to do with surges or grid instability.